Also adding a check to see if this value has been updated frame to frame to allow the frontend to update timings. For example: invadpt2, generate a 0-byte invadpt2. BIOS fallback support LRMAME Plus See changelog here.

The Game Boy palettes that have been received an update are: Super Saiyan God, Super Saiyan Blue, Super Saiyan, Super Saiyan 3, and AKB48 Pink. Plus, Pepsi Blue from here on out is called Pepsi-Cola Blue, to avoid name confusion with the actual Pepsi Blue soft drink.

It turns out the SideM Green palette was in the incorrect shade all this time until now. TWB64 and TWB64 Updated!

Once again, I had to do some deep digging into color research, but just in the Super Dragon Ball Heroes webpages, but regarding Super Saiyan Blue Evolved, the sprite assets from Dragon Ball Z: Dokkan Battle. NeoCD Preliminary support for direct CD-ROM access Enabled LTO for some platforms experimental Reduce latency by adjusting emulated frame slice boundary. Also changed the inputs while the automap is opened, so the player can still move with overlay or if the normal automap is opened but the pause option is OFF.

Changed 2 default values, show walls on normal automap and pause while normal automap is open are ON by default now. Several memory usage improvements. Mainly meant for RS90 but improving other targets as well Decrease internal resolution to × on RS90 Disable adlib on rs90 Synthesize speaker on the fly. Update valid extensions to everything in the core info; Disallow libretro from looking into ZIP files, we will be handling it ourself so that we can load all PRCs and PDBs.

Include miniz library; Make all CMake builds PIC. RetroArch CMake corrections; Implement loading from ZIP files which contain PRCs and PDBs. NOTE: To load multiple files at once, place PRCs and PDBs into a ZIP file and then load that ZIP file. PDBs will be installed first followed by PRC files. NOTE: Enhanced per-tile vertical scroll — This emulation hack allows allows each cell to be vscrolled individually, instead of being limited to 2-cell 16px. The offset of the new, intermediary cell is calculated as an average of the offset of the current 2-cell and the offset of the next 2-cell.

CDI NVRAM is extremely small, so saving to it becomes an issue when you have many games. NOTE: Since it has been a very long time since the last core progress update report, there will be a Core Progress report very soon listing all the changes over the past 6 months that have been made to all the cores in our repertoire. So stay tuned for that blog post. You will get haptic feedback when pressing any of the overlay gamepad elements onscreen, improving the user experience.

In addition, several big improvements are being made under the hood to improve and refine overlay touchscreen controls. We have left this setting on since when frame time spikes were dreadful on Android due to SoCs being underpowered and tons of processes running in the background. Threaded video can theoretically be faster than non-threaded video but also leads to more judder and less precise frame times.

Note — another benefit of non-threaded video being the default is that it fixes some issues that were experienced upon focus loss of an app and re-entering RetroArch.

Thanks to the new Swift backend targeting iOS 13 and up, it has become easier to add several new QoL features, such as iPad trackpad support for iOS Users upgrading to the recent macOS Ventura would have discovered that RetroArch had issues going into fullscreen. This has been fixed in this newer version. Several gamepad overlays have already been updated to take advantage of these new features. These are as follows:.

whether to show eightway settings or not. These allow stretching or shrinking hitboxes and handling their overlap. This simplifies designating animation-only descriptors e. for eightway areas or obsolete descriptors. PS1 and PS2 content scanning has been improved significantly in RetroArch. All PS2 discs should now be able to be scanned. Previously, only CD-based PS2 games could be scanned and not DVD-based ones.

PS1 content scanning has also been improved. More content should be able to be recognized now that the system is also able to scan PSX. EXE files on a disc. Also, all LSP- titles were previously ignored, which has also been fixed. After RetroArch 1. crt-easymode-halation or newpixie. To fix this now with the Vulkan driver, we only skip the tonemapper if HDR10 is explicitly enabled by the last shader pass.

Otherwise, we are simply just inheriting the bit-depth of the swapchain. This view lists all games in your collection released in the year There is now an entirely new way to display and organize content — Views! This also adds the ability to filter a category by range in the Explore menu and not just filter on exact matches. The views are saved into. lvw libretro view files that just like playlist. lpl libretro playlist files are in JSON format and are stored in the same playlists directory.

These are just some examples of what is possible with this new system. The iOS ARM64 port is completely revamped and targets iOS 13 and later now. It leverages Swift and it has some unique features. For instance, it adds support for revealing the onscreen keyboard and enabling touch screen mouse input by adding a toolbar that is revealed by tapping the top of the screen.

Some important WiiU platform improvements. Default directories should now be created on the fly fixing a longstanding issue , and some of the networking issues that popped up in 1. x have now been fixed. NOTE: The Android version on Samsung Galaxy Store, Huawei AppGallery, and Amazon App Store will be updated soon.

We will remove this notice when it has been updated. Until then, grab the APK from our site. NOTE: Several size optimizations have been made to the packages. We no longer pre-install all of the optional XMB theme packs or other miscellaneous assets. Previously we also shipped autoconfig files that were irrelevant for that specific platform. This will install all assets. Debug marker is deprecated years ago. RetroArch keeps introducing innovations to the retrogaming world, constantly building simple roads for players to enjoy classic games in new and sometimes better ways.

Getting the sweet spot between ease of use and customization can be a time-consuming process, and sometimes requires a deep insight of how old technologies worked: refresh rate, aspect ratio, scaling, overscan, deconvergence are terms which we may or may not be familiar with, and these all play an important part in building a retro gaming experience that feels better, yet passionately authentic.

Building an idealized CRT cathode ray tube like display experience. Making it incredibly easy to customize, and yet performant. A fresh and unique starting point for the retro game lover. The Mega Bezel Project started back in July when developer HyperspaceMadness was looking at experimental shaders creating real-time reflections on emulated display bezels. More than two years later, the swiss-army-knife of visual simulation to enhance the retro game experience is ready for players!

The Mega Bezel is unique in that it bends the common definitions of shaders and overlays in an out-of-the-box experience: custom calculations take care of games native resolution and scaling, dynamically draw bezels around the gameplay area filled with curvature simulation and reflections, incorporating a unique pipeline of CRT simulation models and other visual conditioning of the game image, color correction, de-dithering, and adding responsive backgrounds and lots of additional features to enjoy.

The shader centralizes a lot of complex tasks and makes them instantly available for all cores: screen rotation and position, horizontal and vertical orientation, zooming, cutting away games black spaces to get a real full-screen, and filling the aspect ratio difference between the emulated screen and your monitor with interesting graphics. Being based on contributions and discussions from the Libretro forums, Mega Bezel is a community project at its heart: shader writers and artists are actively developing features and customized presets which max out the shader capabilities, and making them freely available for retro players to enjoy and further customize, chasing the their ideal setup.

Easy to use for newcomers, deep in customization for emulation maniacs, flexible for artists: the Mega Bezel project is a fun ongoing journey that strives to bring wonderful features to everyone, minus the hassle of setup! Be sure to read the setup portion of the ReadMe. A small group of talented artists has also come together using the Mega Bezel to create suites of shader presets with beautiful graphics covering many consoles, computers and PVMs to share with retro gamers.

RetroArch is now available from the Windows Package Manager see here. First, start up the Command Prompt. Once on the command line, you can search for packages to see if they exist.

To search for RetroArch, tyep in the following:. Now that we know the package exists on the package manager, we should be able to install this. Simply type on the commandline:. It will now install RetroArch without requiring any user interaction. Once installed, you should be able to find it from the Start Menu as a recently added application. Uninstalling RetroArch once installed is similarly easy. Simply type the following on the commandline:.

Our aim with RetroArch is to be available on as many storefronts and outlets as possible. We have made some impressive progress over the years. We keep expanding! For free, of course. The Galaxy Store should be pre-installed by default on Samsung phones.

It is a storefront available exclusively for Samsung-branded devices. The version available on the Galaxy Store is identical to the version you can download from our website. For RetroArch Plus on the Play Store, it is up to cores that can be installed. We have to hand-pick these cores specifically so that users can install them on the Google Play Store.

There are far more cores available than on the Play Store. On a Samsung phone, you have the choice to choose between either version. Regardless, we highly recommend you use the Galaxy Store version over the Google Play Store version.

Bottom line, we anticipate the Google Play Store version to become more and more nerfed as time goes on unfortunately. There is nothing we can do about this, these are restrictions and limitations imposed by Google to have the software available for distribution on the Play Store.

To get a more full-featured version, download the Galaxy Store version. RetroArch should now be available on the Google Play Store , Amazon App Store , Huawei App Gallery , and Samsung Galaxy Store. No matter what device you are on and which ecosystem you are in, we try to have you covered.

New version of Lakka has been released! We are happy to announce the new and updated version of Lakka. Read the full article here. LRMAME updated to version 0. LRMAME is now also available for ARM Macs now. You can get it from the Core Downloader. The Lightrec dynamic recompiler has been updated, and it should fix several crashes and bugs that occurred before.

These versions can run on older Windows OS versions than the regular version. The gpSP Libretro core now uses a small translation cache for the Miyoo platform. The SMS Plus GX Libretro core should now be more stable on RetroArch PSP. We achieve this by avoiding unaligned memory access. Previously, after starting a game, the console would have a tendency to locks itself and shut down. This fixes Master System background rendering.

It was dropped from 3DS as ARMv6 allows unaligned memory access and defining that macro had no effect anyway. We now ensure that the audio batch callback is only used once per frame unless the frontend does not support batches of sufficient size, in which case the samples will be split appropriately. Several serious crashes should be fixed now as a result of us updating the libco coroutines middleware library.

Add newly- re assigned mappers and Add new mapper We have simply wired it up to a new Audio RF Filter core option. When enabled, the subjective improvement in audio quality is quite dramatic. The filter has a negligible performance impact. The delay can be configured from 1 to 32 ms. minivmac is an emulator for the Mini vMac, a miniature Macintosh. We added this core now for ARM Macs. It can be downloaded from the Core Downloader.

We are using the low memory codepath now for Miyoo systems. As this platform only has 32MB RAM, like the RS This Super NIntendo Entertainment System emulator core has seen several improvements. Before, the core would upload samples in batches of ~64, which means the audio batch callback is used many ~9 times per frame. We have fixed the issue by ensuring that the audio batch callback is used to send all available samples only once per frame. e whenever save states are used , the core determines the save state size by allocating a temporary 5 MB buffer and writing into this an actual save state.

Moreover, it then fails to report the actual size correctly due to a bug in the memory stream wrapper code — which means save states are always 5 MB in size. This represents a terrible inefficiency. Now, the save state size is now calculated independently of regular save state creation. No temporary buffer is required, and there is no need to actually write a save state to memory — and save states now have the correct size ~ kb. At present the core runs at ~75Hz, matching the native refresh rate of the WonderSwan hardware.

This is fine if the core is run on a VRR display or one that natively supports 75Hz… , but on regular 60Hz panels it can cause issues. In particular, screen tearing is very likely to occur. You can experience this on Linux when not using a compositor and without vsync forced at the driver level and on 3DS. The tearing is so bad on 3DS that we would previously consider the core to be unusable on that platform….

We now added a new 60Hz Mode core option, which can be used to force the core to run at 60Hz actually This reduces video smoothness, but then 75Hz on a 60Hz display is not smooth either. More importantly, enabling this option eliminates screen tearing. As further research directions, we have addressed a couple of open problems arose naturally during this work and which depend on its results.

The focus of this letter is on the reduction of the large pilot overhead in orthogonal frequency division multiplexing OFDM based massive multiple-input multiple-output MIMO systems. We propose a novel joint channel estimation and equalization technique that requires only one pilot subcarrier, reducing the pilot overhead by orders of magnitude. We take advantage of the coherent bandwidth spanning over multiple subcarrier bands. This allows for a band of subcarriers to be equalized with the channel frequency response CFR at a single subcarrier.

Subsequently, the detected data symbols are considered as virtual pilots, and their CFRs are updated without additional pilot overhead. Thereafter, the remaining channel estimation and equalization can be performed in a sliding manner. With this approach, we use multiple channel estimates to equalize the data at each subcarrier. This allows us to take advantage of frequency diversity and improve the detection performance.

Finally, we corroborate the above claims through extensive numerical analysis, showing the superior performance of our proposed technique compared to conventional methods. We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the accuracy achieved in a specific iteration with the discretization accuracy of the same iteration.

Apart from the computational advantage, the new modified methods allow to naturally perform p-adaptivity, stopping the iterations when appropriate conditions are met. Moreover, the modification is very easy to be included in an existing implementation of an arbitrary high order iterative scheme and it does not ruin the possibility of parallelization, if this was achievable by the original method. An application to the ADER method for hyperbolic Partial Differential Equations PDEs is presented here.

We explain how such framework can be interpreted as an arbitrary high order iterative scheme, by recasting it as a Deferred Correction DeC method, and how to easily modify it to obtain a more efficient formulation, in which a local a posteriori limiter can be naturally integrated leading to p-adaptivity and structure preserving properties. Finally, the novel approach is extensively tested against classical benchmarks for compressible gas dynamics to show the robustness and the computational efficiency.

The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography CT. In this work, we investigate simple, but yet still provably convergent approaches to learning linear regularization methods from data. More specifically, we analyze two approaches: One generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of [1], and one tailored approach in the Fourier domain that is specific to CT-reconstruction.

We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on. Finally, we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically, discuss their advantages and disadvantages and investigate the effect of discretization errors at different resolutions.

In this paper we give the basic concepts of the geometric theory of composition operators on Sobolev spaces. The main objects are topological mappings which generate the bounded embedding operators on Sobolev spaces by the composition rule. This theory is in some sense a "generalization" of the theory of quasiconformal mappings, but the theory of composition operators is oriented to its applications to the Sobolev embedding theorems, the spectral theory of elliptic operators and the continuum mechanics problems.

We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite.

The potential infinite is understood as a dynamic notion, being an indefinitely extensible finite. The main adoption is the interpretation of the universal quantifier, which has an implicit reflection principle. Each universal quantification refers to an indefinitely large, but finite set.

The quantified sets may increase, so after a reference by quantification, a further reference typically uses a larger, still finite set. We present the concepts for classical first-order logic and show that these dynamic models are sound and complete with respect to the usual inference rules. Moreover, a finite set of formulas requires a finite part of the increasing model for a correct interpretation.

We obtain a Uniqueness Theorem for the problem and a criterion of its solvability in terms of the real-analytic continuation of parabolic potentials, associated with the Cauchy data. We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical weight distribution.

In this context, we establish a duality theorem analogous to but very different from a MacWilliams identity. As an application of our results, we obtain two new bounds for the parameters of a locally recoverable code, including an LP bound that improves on the best available bounds in several instances. We obtain a factorization of the characteristic function of a contractive two-step iterated lifting in terms of the characteristic functions of constituent liftings of the iterated lifting and the Julia-Halmos matrix.

We also give an expression for the characteristic function of the minimal part of a contractive two-step iterated lifting as a restriction of the product of the characteristic functions of constituent liftings of the iterated lifting. Iterative detection and decoding IDD is known to achieve near-capacity performance in multi-antenna wireless systems. We propose deep-unfolded interleaved detection and decoding DUIDD , a new paradigm that reduces the complexity of IDD while achieving even lower error rates.

DUIDD interleaves the inner stages of the data detector and channel decoder, which expedites convergence and reduces complexity. Furthermore, DUIDD applies deep unfolding to automatically optimize algorithmic hyperparameters, soft-information exchange, message damping, and state forwarding.

We demonstrate the efficacy of DUIDD using NVIDIA's Sionna link-level simulator in a 5G-near multi-user MIMO-OFDM wireless system with a novel low-complexity soft-input soft-output data detector, an optimized low-density parity-check decoder, and channel vectors from a commercial ray-tracer. Our results show that DUIDD outperforms classical IDD both in terms of block error rate and computational complexity.

In this paper, we develop further the properties of the refined scissors congruence group in order to extend this result to the case of imaginary quadratic number fields whose ring of integers is a Euclidean domain with respect to the norm. We also obtain stability results for Kleitman's isodiametric inequality and families with bounded set-wise differences. The aim of this paper is to prove that a generalization of those functional identities hold in arbitrary genus.

This allows us to reinterpret the zeta functions as dual versions of the special functions. Moreover we study also the multiplicity of solutions to the associated normalized problem. However, the classical results only showed the finite existence of the solution.

Follow the work by D. The methods in the paper can also be extended to the Euler equations with general time-decay damping. As an corollary, we can derive Liouville theorem for these maps under some finite energy conditons.

An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the system stable in probability.

Sufficient conditions of the stability in probability are obtained, using the second Lyapunov method, in which the construction of the corresponding functions plays an important role. Here we provide a solution to the problem of optimal stabilization in a general case. For a linear system with a quadratic quality function, we give a method of synthesis of optimal control based on the solution of Riccati equations.

Finally, in an autonomous case, a system of differential equations was constructed to obtain unknown matrices that are used for the building of an optimal control. The method of a small parameter is justified for the algorithmic search of an optimal control. This approach brings a novel solution to the problem of optimal stabilization for a stochastic dynamical system with a random structure, Markov switches and Poisson perturbations.

With the increase in the size of the antenna array, the characteristics of the spherical wavefront in the near-field situation are not negligible. Therefore, it is necessary to design a codebook that is adaptive to near-field scenarios.

In this letter, we investigate the hierarchical codebook design method in the near-field situation. We develop a steering beam gain calculation method and design the lower-layer codebook to satisfy the coverage of the Fresnel region. For the upper-layer codebook, we propose beam rotation and beam relocation methods to place an arbitrary beam pattern at target locations. The simulation results show the superiority of the proposed near-field hierarchical codebook design.

We prove that the maximum length of an irredundant base for a primitive action of a finite simple group of Lie type is bounded above by a function which is a polynomial in the rank of the group. We give examples to show that this type of upper bound is best possible. In order to do this we must define and exploit a variety of different ways of constructing elements in the Picard group, and this requires a significant exploration of the theory.

We show that the fundamental group of every enumeratively rationally connected closed symplectic manifold is finite. In other words, if a closed symplectic manifold has a non-zero Gromov-Witten invariant with two point insertions, then it has finite fundamental group. We also show that if the spherical homology class associated to such a non-zero Gromov-Witten invariant is holomorphically indecomposable, then the rational second homology of the symplectic manifold has rank one.

We are studying spatial mappings that satisfy some space analog of a hydrodynamical type of growth in the neighborhood of the infinity. It is proved that homeomorphisms of the specified class form equicontinuous families under some conditions on their characteristic of quasiconformality.

We have also considered the problem of closeness of these classes with respect to locally uniform convergence. We have obtained corresponding results for mappings with integral constraints, as well as for classes of corresponding inverse mappings.

In order to prove the aforementioned uniqueness statement for the ribbon Grothendieck-Verdier structure, we derive a seven-term exact sequence characterizing the space of ribbon Grothendieck-Verdier structures on a balanced braided category.

It was introduced by the paper's last two authors and di Brino as a suitable framework for a coordinate-free study of the Batalin-Vilkovisky complex and more generally for the study of non-linear partial differential equations and their symmetries. The first half of this work was done. We prove that torsion-free, residually finite groups that are inner-amenable and non-amenable have the cheap 1-rebuilding property. This extends results previously known for amenable groups to inner-amenable groups.

We use a structure theorem of Tucker-Drob for inner-amenable groups showing the existence of a chain of q-normal subgroups. This is a case study of teaching 3D design and 3D printing in a project-based computing course for undergraduate math majors. This article discusses content organization, implementation, project grading, and includes a personal reflection. There is an emphasis on lessons learned and how to encourage student creativity and artistic expression.

An appendix details 3D design techniques in Mathematica. In the control of vehicular platoons, the disturbances acting on one vehicle can propagate and affect other vehicles. If the disturbances do not amplify along the vehicular string, then it is called string stable. However, it is usually difficult to achieve string stability with a distributed control setting, especially when a constant spacing policy is considered. This implies that disturbance propagation can be reduced by increasing communication range.

Numerical simulation is provided to illustrate the main results. In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold smooth variety to varieties with rational singularities and prove basic properties of such objects. Moreover, as an application of developed tools, we show that any singular projective contact threefold admits a resolution by a projectivization of the cotangent bundle of some ruled surface.

Integrated Sensing and Communication ISAC systems are recognised as one of the key ingredients of the sixth generation 6G network. A challenging topic in ISAC is the design of a single waveform combining both communication and sensing functionalities on the same time-frequency-space resources, allowing to tune the performance of both with partial or full hardware sharing. This paper proposes a dual-domain waveform design approach that superposes onto the frequency-time FT domain both the legacy orthogonal frequency division multiplexing OFDM signal and a sensing one, purposely designed in the delay-Doppler domain.

With a proper power downscaling of the sensing signal w. OFDM, it is possible to exceed regulatory bandwidth limitations proper of legacy multicarrier systems to increase the sensing performance while leaving communication substantially unaffected. Numerical and experimental results prove the effectiveness of the dual-domain waveform, notwithstanding a power abatement of at least 30 dB of the signal used for sensing compared to the one used for communication.

The method uses an integral representation for the constants and evaluates the integral by applying the double exponential DE quadrature method near the saddle points of the integrands. Further, we provide a highly accurate asymptotic formula for the generalized Stieltjes constants.

We establish the local-to-global property of the synthetic curvature-dimension condition for locally finite metric-measure spaces, extending the work [F. Cavalletti, E. Milman Invent. Thanks to the study of a spectral sequence we get to a computation in low degrees, with remarkable consequences at the level of generic cohomology.

This provides us with a better lifting of elementary embeddings to symmetric extension. In particular, this allows us to more easily lift weakly compact embedding and thus preserve the notion of weakly critical cardinals. We use this improved lifting criterion to show that the first measurable cardinal can be the first weakly critical cardinal or the first Mahlo cardinal, both relative to the existence of a single measurable cardinal.

A natural conjecture for the equivalence between the log-concavity of the Wright function and the existence of such generalized entropies is formulated. In Moser published a simplified version of his proof of the parabolic Harnack inequality.

Moreover, the proposed argument gives a geometric interpretation of Moser's result and could allow transferring Moser's method to other equations.

This work considers a Stokes flow in a deformable fracture interacting with a linear elastic medium. To this end, we employ a phase-field model to approximate the crack dynamics. Phase-field methods belong to interface-capturing approaches in which the interface is only given by a smeared zone. For multi-domain problems, the accuracy of the coupling conditions is, however, of utmost importance.

Here, interface-tracking methods are preferred. The key objective of this work is to construct a robust framework that computes first a crack path via the phase-field method interface-capturing and then does an interface-tracking reconstruction.

We then discuss several approaches to reconstruct the Eulerian description of the open crack domain. This includes unfitted approaches where a level-set of the crack interface is constructed and an approach where the geometry is re-meshed.

Using this reconstructed domain, we can compute the fluid-structure interaction problem between the fluid in the crack and the interacting solid. With the explicit mesh reconstruction of the two domains, we can then use an interface-tracking Arbitrary-Lagrangian-Eulerian ALE discretisation approach for the resulting fluid-structure interaction FSI problem.

Our algorithmic procedure is realised in one final algorithm and one program. We substantiate our approach using several numerical examples based on Sneddon's benchmark and corresponding extensions to Stokes fluid-filled regimes. These examples give a negative answer to the uniqueness problem by Nitsche and Wente of whether any annular solution to the partitioning problem in the ball should be rotational.

Linearized Reed-Solomon LRS codes are a class of evaluation codes based on skew polynomials. They achieve the Singleton bound in the sum-rank metric, and therefore are known as maximum sum-rank distance MSRD codes. In this work, we give necessary and sufficient conditions on the existence of MSRD codes with support-constrained generator matrix. These conditions are identical to those for MDS codes and MRD codes.

The special cases of the result coincide with the known results for Reed-Solomon codes and Gabidulin codes. Graph comparison is a certain type of condition on metric space encoded by a finite graph. We show that any nontrivial graph comparison implies one of two Alexandrov's comparisons.

The proof gives a complete description of graphs with trivial graph comparisons. We show that these infinitary-logic expansions are tame in the sense that they preserve and reflect both the Embedding Ramsey Property ERP and the Modelling Property MP. We then turn our attention to Scow's theorem connecting generalised indiscernibles with Ramsey classes, and show that by passing through infinitary logic, one can obtain a stronger result, which does not require any technical assumptions.

In the final sections of the paper, we also discuss a generalisation of ERP to classes that are no longer required to contain only finite structures, and some relevant weakenings of the ERP. Consequently, the existence of unique strong solutions is obtained for this class of stochastic Volterra equations. This paper presents the preliminary considerations of the application of a software to an experimental work conducted on Digital Storytelling in Mathematics, as part of the project Prin "Digital Interactive Storytelling in Mathematics: a competence-based social approach".

An activity designed for promoting critical mathematical thinking among the students that foresees them to participate as active protagonists and as observers of the protagonists during the problem-solving activity, will be illustrated and then the outcomes will be examined from a numerical analysis point of view. In particular, the interactions between the participants will be investigated by using a Matlab software for solving the seriation problem.

In this paper we study the statistical efficiency of this approach in light of near-term quantum computing. In particular, we propose and analyze a more practically-implementable variant of the protocol, thrifty shadow estimation, in which quantum circuits are reused many times instead of having to be freshly generated for each measurement as in the original protocol. We show that the effect of this reuse strongly depends on the family of quantum circuits that is chosen.

In particular, it is maximally effective when sampling Haar random unitaries, and maximally ineffective when sampling Clifford circuits even though the Clifford group forms a three-design. To interpolate between these two extremes, we provide an efficiently simulable family of quantum circuits inspired by a recent construction of approximate t-designs. Finally we consider tail bounds for shadow estimation and discuss when median-of-means estimation can be replaced with standard mean estimation.

Independence testing is a fundamental and classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should a allow stopping earlier on easy tasks and later on harder tasks , hence making better use of available resources, and b continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate.

It is well known that classical batch tests are not tailored for streaming data settings, since valid inference after data peeking requires correcting for multiple testing, but such corrections generally result in low power. In this paper, we design sequential kernelized independence tests SKITs that overcome such shortcomings based on the principle of testing by betting.

We exemplify our broad framework using bets inspired by kernelized dependence measures such as the Hilbert-Schmidt independence criterion HSIC and the constrained-covariance criterion COCO.

Importantly, we also generalize the framework to non-i. time-varying settings, for which there exist no batch tests. We demonstrate the power of our approaches on both simulated and real data. Methods of pattern recognition and machine learning are applied extensively in science, technology, and society.

Hence, any advances in related theory may translate into large-scale impact. Here we explore how algorithmic information theory, especially algorithmic probability, may aid in a machine learning task. We study a multiclass supervised classification problem, namely learning the RNA molecule sequence-to-shape map, where the different possible shapes are taken to be the classes.

The primary motivation for this work is a proof of concept example, where a concrete, well-motivated machine learning task can be aided by approximations to algorithmic probability. Our approach is based on directly estimating the class i. Naturally, with a large amount of training data, the prior has no significant influence on classification accuracy, but in the very small training data regime, we show that using the prior can substantially improve classification accuracy.

To our knowledge, this work is one of the first to demonstrate how algorithmic probability can aid in a concrete, real-world, machine learning problem. We use causality to derive a number of simple and universal constraints on dispersion relations, which describe the location of singularities of retarded two-point functions in relativistic quantum field theories.

We prove that all causal dissipative dispersion relations have a finite radius of convergence. We then give bounds on all transport coefficients in units of this radius, including an upper bound on diffusivity.

We study three-dimensional quantum field theories on the interval with symmetry-preserving boundary conditions. The physics and symmetries of the effective 2D theory in the IR are the main subjects of this note. We focus on the super- Yang-Mills-Chern-Simons YM-CS theories with the Dirichlet boundary conditions on both ends.

We compute its perturbatively exact two-derivative effective action i. We also construct the 2D Landau-Ginzburg models flowing to the similar sigma models.

Significant advances were made in recent years on the global evolution problem for self-gravitating massive matter in the small-perturbative regime close to Minkowski spacetime. We give here an outline of this method, together with a full proof for a wave-Klein-Gordon model which retains some main challenges arising with the Einstein-matter system.

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J.

Cohen et al. ICLR , which exhibit startling new phenomena the "edge of stability" or "unstable convergence" and potential benefits for generalization in the large learning rate regime. Despite a flurry of recent works on this topic, however, the latter effect is still poorly understood. In this paper, we take a step towards understanding genuinely non-convex training dynamics with large learning rates by performing a detailed analysis of gradient descent for simplified models of two-layer neural networks.

For these models, we provably establish the edge of stability phenomenon and discover a sharp phase transition for the step size below which the neural network fails to learn "threshold-like" neurons i. This elucidates one possible mechanism by which the edge of stability can in fact lead to better generalization, as threshold neurons are basic building blocks with useful inductive bias for many tasks.

Boundary conditions BCs are important groups of physics-enforced constraints that are necessary for solutions of Partial Differential Equations PDEs to satisfy at specific spatial locations. These constraints carry important physical meaning, and guarantee the existence and the uniqueness of the PDE solution. Current neural-network based approaches that aim to solve PDEs rely only on training data to help the model learn BCs implicitly.

There is no guarantee of BC satisfaction by these models during evaluation. In this work, we propose Boundary enforcing Operator Network BOON that enables the BC satisfaction of neural operators by making structural changes to the operator kernel.

We provide our refinement procedure, and demonstrate the satisfaction of physics-based BCs, e. Dirichlet, Neumann, and periodic by the solutions obtained by BOON. Numerical experiments based on multiple PDEs with a wide variety of applications indicate that the proposed approach ensures satisfaction of BCs, and leads to more accurate solutions over the entire domain. In studies of one-dimensional Bethe ansatz solvable models, a Fredholm integral equation of the second kind with a difference kernel on a finite interval often appears.

This equation does not generally admit a closed-form solution and hence its analysis is quite complicated. Here we study a family of such equations concentrating on their moments. We find exact relations between the moments in the form of difference-differential equations. The latter results significantly advance the analysis, enabling one to practically determine all the moments from the explicit knowledge of the lowest one. As applications, first we study the moments of the quasimomentum distribution in the Lieb-Liniger model and find explicit analytical results.

The latter moments determine several basic quantities, e. We prove the equivalence between different expressions found in the literature for the three-body local correlation functions and find an exact result for the four-body local correlation function in terms of the moments of the quasimomentum distributions.

We eventually find the analytical results for the three- and four-body correlation functions in the form of asymptotic series in the regimes of weak and strong interactions.

Next, we study the exact form of the low-energy spectrum of a magnon a polaron excitation in the two-component Bose gas described by the Yang-Gaudin model.

We find its explicit form, which depends on the moments of the quasimomentum distributions of the Lieb-Liniger model. Then, we address a seemingly unrelated problem of capacitance of a circular capacitor and express the exact result for the capacitance in the parametric form.

In the most interesting case of short plate separations, the parametric form has a single logarithmic term. This should be contrasted with the explicit result that has a complicated structure of logarithms. We study a class of Galilean-invariant one-dimensional Bethe ansatz solvable models in the thermodynamic limit.

Their rapidity distribution obeys an integral equation with a difference kernel over a finite interval, which does not admit a closed-form solution. We develop a general formalism enabling one to study the moments of the rapidity distribution, showing that they satisfy a difference-differential equation.

The derived equation is explicitly analyzed in the case of the Lieb-Liniger model and the moments are analytically calculated. In addition, we obtained the exact information about the ground-state energy at weak repulsion. The obtained results directly enter a number of physically relevant quantities.

Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering.

The crucial computing kernel for such iterative solutions is the multiplication of a sparse matrix by a dense vector. Efficient implementation of sparse matrix-vector multiplication SpMV and linear solvers are therefore essential and has been subjected to extensive research across a variety of computing architectures and accelerators such as central processing units CPUs , graphical processing units GPUs , many integrated cores MICs , and field programmable gate arrays FPGAs.

This article presents the first of its kind, in-depth survey covering over two hundred state-of-the-art optimization schemes for solving sparse iterative linear systems with a focus on computing SpMV. A new taxonomy for iterative solutions and SpMV techniques common to all architectures is proposed. This article includes reviews of SpMV techniques for all architectures to consolidate a single taxonomy to encourage cross-architectural and heterogeneous-architecture developments.

However, the primary focus is on GPUs. The major contributions as well as the primary, secondary, and tertiary contributions of the SpMV techniques are first highlighted utilizing the taxonomy and then qualitatively compared.

A summary of the current state of the research for each architecture is discussed separately. Finally, several open problems and key challenges for future research directions are outlined. In recent years it has become evident the need of understanding how failure of coordination imposes constraints on the size of stable groups that highly social mammals can live in.

We examine here the forces that keep animals together as a herd and others that drive them apart. Different phenotypes e. genders have different rates of gut fill, causing them to spend different amounts of time performing activities. By modeling a group as a set of semi-coupled oscillators on a disc, we show that the members of the group may become less and less coupled until the group dissolves and breaks apart.

We show that when social bonding creates a stickiness, or gravitational pull, between pairs of individuals, fragmentation is reduced. In this paper, we formulate three nonintrusive methods and systematically explore their performance in terms of the ability to reconstruct the quantities of interest and their predictive capabilities.

The methods include deterministic dynamic mode decomposition DMD , randomized DMD and nonlinear proper orthogonal decomposition NLPOD. We apply these methods to a convection dominated fluid flow problem governed by the Boussinesq equations. We analyze the reconstruction results primarily at two different times for considering different noise levels synthetically added into the data snapshots. Overall, our results indicate that, with a proper selection of the number of retained modes and neural network architectures, all three approaches make predictions that are in a good agreement with the full order model solution.

However, we find that the NLPOD approach seems more robust for higher noise levels compared to both DMD approaches. In manufacturing, the production is often done on out-of-the-shelf manufacturing lines, whose underlying scheduling heuristics are not known due to the intellectual property. We consider such a setting with a black-box job-shop system and an unknown scheduling heuristic that, for a given permutation of jobs, schedules the jobs for the black-box job-shop with the goal of minimizing the makespan.

Here, the jobs need to enter the job-shop in the given order of the permutation, but may take different paths within the job shop, which depends on the black-box heuristic. The performance of the black-box heuristic depends on the order of the jobs, and the natural problem for the manufacturer is to find an optimum ordering of the jobs.

Facing a real-world scenario as described above, we engineer the Monte-Carlo tree-search for finding a close-to-optimum ordering of jobs. To cope with a large solutions-space in planning scenarios, a hierarchical Monte-Carlo tree search H-MCTS is proposed based on abstraction of jobs.

On synthetic and real-life problems, H-MCTS with integrated abstraction significantly outperforms pure heuristic-based techniques as well as other Monte-Carlo search variants. We furthermore show that, by modifying the evaluation metric in H-MCTS, it is possible to achieve other optimization objectives than what the scheduling heuristics are designed for -- e.

Our experimental observations have been also validated in real-life cases, and our H-MCTS approach has been implemented in a production plant's controller. Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis.

The representation of these sets is a key factor that affects the computational complexity and the approximation error. In this paper, we develop a new approach for over-approximating the reachable sets of neural network dynamical systems using adaptive template polytopes. We use the singular value decomposition of linear layers along with the shape of the activation functions to adapt the geometry of the polytopes at each time step to the geometry of the true reachable sets.

We then propose a branch-and-bound method to compute accurate over-approximations of the reachable sets by the inferred templates. We illustrate the utility of the proposed approach in the reachability analysis of linear systems driven by neural network controllers. We propose a definition of a diffiety based on the theory of Frolicher structures.

As a consequence, we obtain a natural Vinogradov sequence and, under the assumption of the existence of a suitable derivation, we can form on it a Kadomtsev-Petviashvili hierarchy which is well-posed. Computing the agreement between two continuous sequences is of great interest in statistics when comparing two instruments or one instrument with a gold standard.

The probability of agreement PA quantifies the similarity between two variables of interest, and it is useful for accounting what constitutes a practically important difference. In this article we introduce a generalization of the PA for the treatment of spatial variables. Our proposal makes the PA dependent on the spatial lag. As a consequence, for isotropic stationary and nonstationary spatial processes, the conditions for which the PA decays as a function of the distance lag are established.

Estimation is addressed through a first-order approximation that guarantees the asymptotic normality of the sample version of the PA. The sensitivity of the PA is studied for finite sample size, with respect to the covariance parameters. The new method is described and illustrated with real data involving autumnal changes in the green chromatic coordinate Gcc , an index of "greenness" that captures the phenological stage of tree leaves, is associated with carbon flux from ecosystems, and is estimated from repeated images of forest canopies.

The paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control Problem OCP , which allows for forward prediction and optimization of statistical distributions of inputs and outputs. Our approach avoids the use of parametric system models.

Instead it is based on previously recorded data using a recently proposed stochastic variant of Willems' fundamental lemma. The stochastic variant of the lemma is applicable to a large class of linear dynamics subject to stochastic disturbances of Gaussian and non-Gaussian nature.

To ensure recursive feasibility, the initial condition of the OCP -- which consists of information about past inputs and outputs -- is considered as an extra decision variable of the OCP.

We provide sufficient conditions for recursive feasibility and closed-loop practical stability of the proposed scheme as well as performance bounds. Finally, a numerical example illustrates the efficacy and closed-loop properties of the proposed scheme. We identify the maximal chiral algebra of conformal cyclic orbifolds.

In terms of this extended algebra, the orbifold is a rational and diagonal conformal field theory, provided the mother theory itself is also rational and diagonal.

The operator content and operator product expansion of the cyclic orbifolds are revisited in terms of this algebra.

The fusion rules and fusion numbers are computed via the Verlinde formula. This allows one to predict which conformal blocks appear in a given four-point function of twisted or untwisted operators, which is relevant for the computation of various entanglement measures in one-dimensional critical systems.

In this paper, we consider the inventory management IM problem where we need to make replenishment decisions for a large number of stock keeping units SKUs to balance their supply and demand. In our setting, the constraint on the shared resources such as the inventory capacity couples the otherwise independent control for each SKU. We formulate the problem with this structure as Shared-Resource Stochastic Game SRSG and propose an efficient algorithm called Context-aware Decentralized PPO CD-PPO.

Through extensive experiments, we demonstrate that CD-PPO can accelerate the learning procedure compared with standard MARL algorithms. The formula is checked by relating hyperbolic representation matrices with the Whittaker function. Skip to content NOWCAST News 9 This Morning a. Live Now. Press enter to search Type to Search. Search location by ZIP code ZIP.

The content you're looking for is no longer available. Daniel Cole. By Associated Press. WMUR Arizona man ticketed for driving in the HOV lane with an inflatable Grinch in the passenger seat WMUR 'Unlike any planets found in our solar system:' These two planets are probably made of water, study finds WMUR.

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Help Advanced Search. In this paper we construct odd finitely summable spectral triples based on length functions of bounded doubling on noncommutative solenoids. Our spectral triples induce a Leibniz Lip-norm on the state spaces of the noncommutative solenoids, giving them the structure of Leibniz quantum compact metric spaces. By applying methods of R.

Floricel and A. Ghorbanpour, we also show that our odd spectral triples on noncommutative solenoids can be considered as direct limits of spectral triples on rotation algebras. In the final section we prove a noncommutative Wiener's lemma and show that our odd spectral triples can be defined to have an associated smooth dense subalgebra which is stable under the holomorphic functional calculus, thus answering a question of B.

Long and W. The construction of the smooth subalgebra also extends to the case of nilpotent discrete groups. Stochastic dominance orders are commonly used in the theory and practice of risk management and decision making under uncertainty.

This characterization establishes a connection between the risk tolerance of decision makers and bounded stochastic dominance orders, and hence, it provides a decision theoretic interpretation for these stochastic orders.

This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners.

Special attention is given to the pull-back product of such smooth maps, which provides our geometric cochains with a partially defined product structure inducing the cup product in cohomology. A parallel treatment of homology is also given allowing for a geometric unification of the contravariant and covariant theories.

The monograph is devoted to the study of stochastic area functionals of Brownian motions and of the associated heat kernels on Lie groups and Riemannian manifolds. It is essentially self-contained and as such can serve as a textbook on the theory of Brownian motions and horizontal Brownian motions on manifolds. Emphasis is put on concrete examples which allows us to concretely illustrate the rich and deep interactions between stochastic calculus, Riemannian and sub-Riemannian geometry, the theory of complex and quaternionic symmetric spaces and random matrices.

We estimate from below the topological entropy of the generalized Bunimovich stadium billiards. We do it for long billiard tables, and find the limit of estimates as the length goes to infinity. We prove the Schwarz-Zaboronsky localization theorem for CS manifolds and use this to give a volume calculation for homogeneous superspaces for super-Lie groups that lack a real form.

We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive dimensions.

We also show other pairs of dimensions for which the last result can be generalized. In this paper we describe the current state of Arnold's problems.

We also consider closely related problems about the Radon transform of indicator functions. In the second part, we will obtain the linearization result, which works for a more general class of Lie algebras. For the proof, we will develop a Nash-Moser method for functions that are flat at a point.

In this second part, we obtain the linearization result, which works for a more general class of Lie algebras. For the proof, we develop a Nash-Moser method for functions that are flat at a point. This turns out to be an elementary exercise in the homotopy of closed curves in three dimensions. The matrices represent gapped Bloch Hamiltonians in 1D with a two-dimensional Hilbert space per unit cell. Privacy protection and nonconvexity are two challenging problems in decentralized optimization and learning involving sensitive data.

The new algorithm allows the incorporation of persistent additive noise to enable rigorous differential privacy for data samples, gradients, and intermediate optimization variables without losing provable convergence, and thus circumventing the dilemma of trading accuracy for privacy in differential privacy design.

More interestingly, the algorithm is theoretically proven to be able to efficiently { guarantee accuracy by avoiding} convergence to local maxima and saddle points, which has not been reported before in the literature on decentralized nonconvex optimization. The algorithm is efficient in both communication it only shares one variable in each iteration and computation it is encryption-free , and hence is promising for large-scale nonconvex optimization and learning involving high-dimensional optimization parameters.

Numerical experiments for both a decentralized estimation problem and an Independent Component Analysis ICA problem confirm the effectiveness of the proposed approach. In a coupled network cells can interact in several ways. There is a vast literature from the last twenty years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence relation on the set of vertices that enables a characterization of the admissible vector fields that rules the network dynamics.

Given a mapping, we present a procedure to construct all non-equivalent admissible graphs, up to the appropriate equivalence relation. We also give an upper bound for the number of such graphs. As a consequence, invariant subspaces under the vector field can be investigated as the locus of synchrony states supported by an admissible graph, in the sense that a suitable graph can be chosen to realize couplings with more or less synchrony than another graph admissible to the same vector field.

The approach provides in particular a systematic investigation of occurrence of chimera states in a network of van der Pol identical oscillators. The Krawtchouck polynomials arise naturally in both coding theory and probability theory and have been studied extensively from these points of view. However, very little is known about their irreducibility and Galois properties. Just like many classical families of orthogonal polynomials e.

the Legendre and Laguerre , the Krawtchouck polynomials can be viewed as special cases of Jacobi polynomials. In this paper we determine the Newton Polygons of certain Krawtchouck polynomials and show that they are very similar to those of the Legendre polynomials and exhibit new cases of irreducibility.

However, we also show that their Galois groups are significantly more complicated to study, due to the nature of their coefficients, versus those of other classical orthogonal families. Previously we showed that the tensor product of a weight module over a generalized Weyl algebra GWA with a weight module over another GWA is a weight module over a third GWA.

In this paper we compute tensor products of simple and indecomposable weight modules over generalized Weyl algebras supported on a finite orbit.

This allows us to give a complete presentation by generators and relations of the Grothendieck ring of the categories of weight modules over a tower of generalized Weyl algebras in this setting. We also obtain partial results about the split Grothendieck ring. We described the case of infinite orbits in previous work. These inequalities yield surgery-stable curvature conditions tailored to annihilate further rational cobordism invariants, such as the Witten genus, elliptic genus, signature, and even the rational cobordism class itself.

We present a different approach to show this property by using the spectral information of the corresponding linearized operator around the periodic solution and tools about the Floquet theory.

We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formulated whose infimum is equal to the maximal Lyapunov exponent when trajectories of interest remain in a compact set. The minimization is over auxiliary functions that are defined on the state space and subject to certain pointwise inequalities. In the polynomial case -- i.

Enlarging the spaces of polynomials over which auxiliary functions are sought yields optimization problems of increasing computational cost whose infima converge from above to the maximal Lyapunov exponent, provided the set of interest is compact and satisfies a mild technical condition. In each example the computed upper bounds converge as polynomial degrees are raised, giving a bound that is sharp to at least five digits.

This sharpness is confirmed by finding trajectories whose leading Lyapunov exponents approximately equal the upper bounds.

We pose reciprocity conjectures of the Chern-Simons invariants of 3-manifolds, and discuss some supporting evidence on the conjectures. The matrix-valued potential is decomposed into a finite number of fragments, and a factorization formula is presented expressing the matrix-valued scattering coefficients in terms of the matrix-valued scattering coefficients for the fragments.

Using the factorization formula, some explicit examples are provided illustrating that in general the left and right matrix-valued transmission coefficients are unequal. Using that unitary transformation, the relations are established between the full-line and the half-line quantities such as the Jost solutions, the physical solutions, and the scattering matrices.

Exploiting the connection between the corresponding full-line and half-line scattering matrices, Levinson's theorem on the full line is proved and is related to Levinson's theorem on the half line.

A number of convergence results on the method are established, and accuracy estimates for approximate singular triplets are given. In finite precision arithmetic, it is proven that the semi-orthogonality of each set of basis vectors and the semi-biorthogonality of two sets of basis vectors suffice to compute the singular values accurately. A commonly used efficient partial reorthogonalization strategy is adapted to maintaining the needed semi-orthogonality and semi-biorthogonality.

For a practical purpose, an implicitly restarted SSLBD algorithm is developed with partial reorthogonalization. Numerical experiments illustrate the effectiveness and overall efficiency of the algorithm.

This problem was first introduced by Aharoni and Berger, and has since been studied by several different authors. We give simple geometric proofs of Aprodu-Farkas-Papadima-Raicu-Weyman's theorem on syzygies of tangent developable surfaces of rational normal curves and Raicu-Sam's result on syzygies of K3 carpets. We also show the arithmetic normality of tangent developable surfaces of arbitrary smooth projective curves of large degree.

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning.

Our algorithmic framework updates the primal variable between the twice calculations of the dual variable, thereby appearing a symmetric iterative scheme, which is accordingly called the symmetric primal-dual algorithm SPIDA.

It is noteworthy that the subproblems of our SPIDA are equipped with Bregman proximal regularization terms, which makes SPIDA versatile in the sense that it enjoys an algorithmic framework covering some existing algorithms such as the classical augmented Lagrangian method ALM , linearized ALM, and Jacobian splitting algorithm for linearly constrained optimization problems.

Besides, our algorithmic framework allows us to derive some customized versions so that SPIDA works as efficiently as possible for structured optimization problems. Theoretically, under some mild conditions, we prove the global convergence of SPIDA and estimate the linear convergence rate under a generalized error bound condition defined by Bregman distance.

Finally, a series of numerical experiments on the matrix game, basis pursuit, robust principal component analysis, and image restoration demonstrate that our SPIDA works well on synthetic and real-world datasets. We first show that the maximum of the landscape function is comparable to the reciprocal of the ground state eigenvalue if the operator satisfies certain semigroup kernel upper bounds. We also numerically study the random hopping model when the band width hopping distance is greater than one, and provide strong numerical evidence that a similar approximation holds for low-lying energies in the spectrum.

This paper presents the vision of multi-band communication networks MBN in 6G, where optical and TeraHertz THz transmissions will coexist with the conventional radio frequency RF spectrum.

This paper will first define the two potential MBN configurations, i. Relevant key performance indicators KPIs in this context will be defined. Then, we highlight the fundamental challenges of MBNs at the PHYsical PHY and Medium Access MAC layer, such as unique propagation characteristics, transceiver design, resource management, traffic offloading, mobility management, etc.

Our results show that stand-alone deployment requires a higher number of BSs compared to integrated deployment in order to achieve a given data rate. Stand-alone deployment, however, offers flexibility and enables controlling the number of access points in different transmission bands.

Finally, open research directions will be presented. In this paper, we study relay selection and power allocation in two-way relaying networks consisting of a source, a destination and multiply half-duplex decode-and-forward DF relays.

A transmission model with three time subslots is purposely introduced. In the first subslot, selected relay applies time-switching protocol to harvest radio frequency energy radiated by source and destination; in the remaining subslots, selected relay facilitates source and destination to exchange information. Due to finite-size data buffer and finite-size battery of relay, an optimal relay selection and power allocation policy is proposed, in order to maximize networks sum-throughput.

One obstacle is the inherent non-convex property of the underlying sum-throughput optimization problem. By carefully decoupling the multiplicative variables and relaxing binary variable to a real number, we convert this problem into a convex optimization one and then Karush-Kuhn-Tucker KKT conditions are used to solve it.

Extensive simulations have been conducted to demonstrate the improved sum-throughput with our proposed strategy. The duality on Legendre singularities is observed related to the pendulum motion. Further more, we obtain a local isoparametric function constructed by a distance function and give a global isoparametric function on a standard Finsler sphere. A competitive resource-consumer dynamical model is analyzed based on a novel Lotka-Volterra model similar to Rosenwig-McArthur one.

cmd used instead of git. Thus the ambiguity in cascaded channel estimation, which may affect optimal passive beamforming, is avoided. PR Using Common Item Dialog to select folders. For now, we'll have to content ourselves with poring over these kinds of corporate submissions for more interesting tidbits like this one. Always use final render pass type equal to swapchain format. Here we incorporate this idea into a novel recurrent neural network RNN training framework for DS reconstruction based on multimodal variational autoencoders MVAE.

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