cssi/SciSciGPT-SciSciNet huggingface dataset:
Stability of interconnected DC converters

This paper addresses stability issues of DC networks with constant power loads (CPL). Common DC networks, such as automotive electrical systems and DC microgrids, typically have a step-up/down converter connected in one side to the main bus and, on the other, to the load. When load is constant power it can generate destabilizing effects if not proper controlled. This paper shows that converters driving CPLs can make the system unstable, even if they are individually stable, depending on network parameters. We mitigate this problem by means of passive components externally connected to the converter/CPL subsystem. The analysis is verified through simulations. We are able to show that certain converter circuit configurations achieve the so called plug-and-play property, which stabilizes the interconnected system for all network parameters. This property is desirable since it is does not require the knowledge of detailed system topology and parameters, which can be time varying and difficult to obtain. This method also contrasts to existing practices of load augmentation, which can lead to severe efficiency losses.
Vertex operator algebras associated to type G affine Lie algebras

Abstract In this paper, we study representations of the vertex operator algebra L ( k , 0 ) at one-third admissible levels k = − 5 3 , − 4 3 , − 2 3 for the affine algebra of type G 2 ( 1 ) . We first determine singular vectors and then obtain a description of the associative algebra A ( L ( k , 0 ) ) using the singular vectors. We then prove that there are only finitely many irreducible A ( L ( k , 0 ) ) -modules from the category O . Applying the A ( V ) -theory, we prove that there are only finitely many irreducible weak L ( k , 0 ) -modules from the category O and that such an L ( k , 0 ) -module is completely reducible. Our result supports the conjecture made by Adamovic and Milas (1995) [2] .
On the Concordance Genus of Topologically Slice Knots

The concordance genus of a knot K is the minimum Seifert genus of all knots smoothly concordant to K. Concordance genus is bounded below by the 4-ball genus and above by the Seifert genus. We give a lower bound for the concordance genus of K coming from the knot Floer complex of K. As an application, we prove that there are topologically slice knots with 4-ball genus equal to one and arbitrarily large concordance genus.
Uniform bounds in F-finite rings and lower semi-continuity of the F-signature

This paper establishes uniform bounds in characteristic $p$ rings which are either F-finite or essentially of finite type over an excellent local ring. These uniform bounds are then used to show that the Hilbert-Kunz length functions and the normalized Frobenius splitting numbers defined on the Spectrum of a ring converge uniformly to their limits, namely the Hilbert-Kunz multiplicity function and the F-signature function. From this we establish that the F-signature function is lower semi-continuous. We also give a new proof of the upper semi-continuity of Hilbert-Kunz multiplicity, which was originally proven by Ilya Smirnov.
Calibrated Manifolds and Gauge Theory

By a theorem of Mclean, the deformation space of an associative submanifold Y of an integrable G_2 manifold (M,\phi) can be identified with the kernel of a Dirac operator D:\Omega^{0}(\nu) -->\Omega^{0}(\nu) on the normal bundle \nu of Y. Here, we generalize this to the non-integrable case, and also show that the deformation space becomes smooth after perturbing it by natural parameters, which corresponds to moving Y through `pseudo-associative' submanifolds. Infinitesimally, this corresponds to twisting the Dirac operator D --> D_{A} with connections A of \nu. Furthermore, the normal bundles of the associative submanifolds with Spin^c structure have natural complex structures, which helps us to relate their deformations to Seiberg-Witten type equations. If we consider G_2 manifolds with 2-plane fields (M,\phi, \Lambda) (they always exist) we can split the tangent space TM as a direct sum of an associative 3-plane bundle and a complex 4-plane bundle. This allows us to define (almost) \Lambda-associative submanifolds of M, whose deformation equations, when perturbed, reduce to Seiberg-Witten equations, hence we can assign local invariants to these submanifolds. Using this we can assign an invariant to (M,\phi, \Lambda). These Seiberg Witten equations on the submanifolds are restrictions of global equations on M. We also discuss similar results for the Cayley submanifolds of a Spin(7) manifold.
DAPPER: Scaling Dynamic Author Persona Topic Model to Billion Word Corpora

Extracting common narratives from multi-author dynamic text corpora requires complex models, such as the Dynamic Author Persona (DAP) topic model. However, such models are complex and can struggle to scale to large corpora, often because of challenging non-conjugate terms. To overcome such challenges, we adapt new ideas in approximate inference to the DAP model, resulting in the DAP Performed Exceedingly Rapidly (DAPPER) topic model. Specifically, we develop Conjugate-Computation Variational Inference (CVI) based variational Expectation-Maximization (EM) for learning the model, yielding fast, closed form updates for each document, replacing iterative optimization in earlier work. Our results show significant improvements in model fit and training time without needing to compromise the model's temporal structure or the application of Regularized Variation Inference (RVI). We demonstrate the scalability and effectiveness of the DAPPER model on multiple datasets, including the CaringBridge corpus — a collection of 9 million journals written by 200,000 authors during health crises.
A Small Universal Petri Net

A universal deterministic inhibitor Petri net with 14 places, 29 transitions and 138 arcs was constructed via simulation of Neary and Woods’ weakly universal Turing machine with 2 states and 4 symbols; the total time complexity is exponential in the running time of their weak machine. To simulate the blank words of the weakly universal Turing machine, a couple of dedicated transitions insert their codes when reaching edges of the working zone. To complete a chain of a given Petri net encoding to be executed by the universal Petri net, a translation of a bi-tag system into a Turing machine was constructed. The constructed Petri net is universal in the standard sense; a weaker form of universality for Petri nets was not introduced in this work.
A Spiking Neural Network with Local Learning Rules Derived from Nonnegative Similarity Matching

The design and analysis of spiking neural network algorithms will be accelerated by the advent of new theoretical approaches. In an attempt at such approach, we provide a principled derivation of a spiking algorithm for unsupervised learning, starting from the nonnegative similarity matching cost function. The resulting network consists of integrate-and-fire units and exhibits local learning rules, making it biologically plausible and also suitable for neuromorphic hardware. We show in simulations that the algorithm can perform sparse feature extraction and manifold learning, two tasks which can be formulated as nonnegative similarity matching problems.
Homological Mirror Symmetry for the genus two curve

Katzarkov has proposed a generalization of Kontsevich's mirror symmetry conjecture, covering some varieties of general type. We prove a version of this conjecture in the simplest example, relating the Fukaya category of a genus two curve to the category of Landau-Ginzburg branes on a certain singular rational surface.
Inner Approximation of Minkowski Sums: A Union-Based Approach and Applications to Aggregated Energy Resources

This paper develops and compares algorithms to compute inner approximations of the Minkowski sum of convex polytopes. As an application, the paper considers the computation of the feasibility set of aggregations of distributed energy resources (DERs), such as solar photovoltaic inverters, controllable loads, and storage devices. To fully account for the heterogeneity in the DERs while ensuring an acceptable approximation accuracy, the paper leverages a union-based computation and advocates homothet-based polytope decompositions. However, union-based approaches can in general lead to high-dimensionality concerns; to alleviate this issue, this paper shows how to define candidate sets to reduce the computational complexity. Accuracy and trade-offs are analyzed through numerical simulations for illustrative examples.
Fuchs' problem for dihedral groups

Abstract More than 50 years ago, Laszlo Fuchs asked which abelian groups can be the group of units of a ring. Though progress has been made, the question remains open. One could equally well pose the question for various classes of nonabelian groups. In this paper, we prove that D 2 , D 4 , D 6 , D 8 , and D 12 are the only dihedral groups that appear as the group of units of a ring of positive characteristic (or, equivalently, of a finite ring), and D 2 and D 4 k , where k is odd, are the only dihedral groups that appear as the group of units of a ring of characteristic 0.
On the Complexity and Approximability of Optimal Sensor Selection for Kalman Filtering

Given a linear dynamical system, we consider the problem of selecting (at design-time) an optimal set of sensors (subject to certain budget constraints) to minimize the trace of the steady state error covariance matrix of the Kalman filter. Previous work has shown that this problem is NP-hard for certain classes of systems and sensor costs; in this paper, we show that the problem remains NP-hard even for the special case where the system is stable and all sensor costs are identical. Furthermore, we show the stronger result that there is no constant-factor (polynomial-time) approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering.
A Convex Sum-of-Squares Approach to Analysis, State Feedback and Output Feedback Control of Parabolic PDEs

We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying coefficients without discretization or numerical approximation. For controller synthesis, we consider both full-state feedback and point observation (output feedback). The input occurs at the boundary (point actuation). We use positive-definite matrices to parameterize positive Lyapunov functions and polynomials to parameterize controller and observer gains. We use duality and an invertible state variable transformation to convexify the controller synthesis problem. Finally, we combine our synthesis condition with the Luenberger observer framework to express the output feedback controller synthesis problem as a set of LMI/SDP constraints. We perform an extensive set of numerical experiments to demonstrate the accuracy of the conditions and to prove the necessity of the Lyapunov structures chosen. We provide numerical and analytical comparisons with alternative approaches to control, including Sturm–Liouville theory and backstepping. Finally, we use numerical tests to show that the method retains its accuracy for alternative boundary conditions.
Efficient inference of Gaussian-process-modulated renewal processes with application to medical event data

The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables (or events) by modeling them as a renewal process and inferring a probability density over non-parametric longitudinal intensity functions that modulate the process. Several methods exist for inferring such a density over intensity functions, but either their constraints prevent their use with our potentially bursty event streams, or their time complexity renders their use intractable on our long-duration observations of high-resolution events, or both. In this paper we present a new efficient and flexible inference method that uses direct numeric integration and smooth interpolation over Gaussian processes. We demonstrate that our direct method is up to twice as accurate and two orders of magnitude more efficient than the best existing method (thinning). Importantly, our direct method can infer intensity functions over the full range of bursty to memoryless to regular events, which thinning and many other methods cannot do. Finally, we apply the method to clinical event data and demonstrate a simple example application facilitated by the abstraction.
Extreme events and their optimal mitigation in nonlinear structural systems excited by stochastic loads: Application to ocean engineering systems

Abstract We develop an efficient numerical method for the probabilistic quantification of the response statistics of nonlinear multi-degree-of-freedom structural systems under extreme forcing events, emphasizing accurate heavy-tail statistics. The response is decomposed to a statistically stationary part and an intermittent component. The stationary part is quantified using a statistical linearization method while the intermittent part, associated with extreme transient responses, is quantified through i) either a few carefully selected simulations or ii) through the use of effective measures (effective stiffness and damping). The developed approach is able to accurately capture the extreme response statistics orders of magnitude faster compared with direct methods. The scheme is applied to the design and optimization of small attachments that can mitigate and suppress extreme forcing events delivered to a primary structural system. Specifically, we consider the problem of suppression of extreme responses in two prototype ocean engineering systems. First, we consider linear and cubic springs and perform parametric optimization by minimizing the forth-order moments of the response. We then consider a more generic, possibly asymmetric, piecewise linear spring and optimize its nonlinear characteristics. The resulting asymmetric spring design far outperforms the optimal cubic energy sink and the linear tuned mass dampers.
Transverse temperature interfaces in the Katz-Lebowitz-Spohn driven lattice gas

We explore the intriguing spatial patterns that emerge in a two-dimensional spatially inhomogeneous Katz-Lebowitz-Spohn (KLS) driven lattice gas with attractive nearest-neighbor interactions. The domain is split into two regions with hopping rates governed by different temperatures T>T_{c} and T_{c}, respectively, where T_{c} indicates the critical temperature for phase ordering, and with the temperature boundaries oriented perpendicular to the drive. In the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region. To explain this particle density accumulation near the interface, we have measured the steady-state current in the KLS model at T>T_{c} and found it to decay as 1/T. In analogy with TASEP systems containing "slow" bonds, we argue that transport in the high-temperature subsystem is impeded by the lower current in the cooler region, which tends to set the global stationary particle current value. This blockage is induced by the extended particle clusters, growing logarithmically with system size, in the critical region. We observe the density profiles in both high- and low-temperature subsystems to be similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_{c}, we detect marked fluctuation corrections to the mean-field density profiles, e.g., the corresponding critical KLS power-law density decay near the interfaces into the cooler region.
A diffusion generated method for computing Dirichlet partitions

Abstract A Dirichlet k -partition of a closed d -dimensional surface is a collection of k pairwise disjoint open subsets such that the sum of their first Laplace–Beltrami–Dirichlet eigenvalues is minimal. In this paper, we develop a simple and efficient diffusion generated method to compute Dirichlet k -partitions for d -dimensional flat tori and spheres. For the two-dimensional flat torus, for most values of k = 3 – 9 , 11 , 12 , 15 , 16 , and 20, we obtain hexagonal honeycombs. For the three-dimensional flat torus and k = 2 , 4 , 8 , 16 , we obtain the rhombic dodecahedral honeycomb, the Weaire–Phelan honeycomb, and Kelvin’s tessellation by truncated octahedra. For the four-dimensional flat torus, for k = 4 , we obtain a constant extension of the rhombic dodecahedral honeycomb along the fourth direction and for k = 8 , we obtain a 24-cell honeycomb. For the two-dimensional sphere, we also compute Dirichlet partitions for k = 3 – 7 , 9 , 10 , 12 , 14 , 20 . Our computational results agree with previous studies when a comparison is available. As far as we are aware, these are the first results for Dirichlet partitions of the four-dimensional flat torus.
The benefit of encoder cooperation in the presence of state information

In many communication networks, the availability of channel state information at various nodes provides an opportunity for network nodes to work together, or “cooperate.” This work studies the benefit of cooperation in the multiple access channel with a cooperation facilitator, distributed state information at the encoders, and full state information available at the decoder. Under various causality constraints, sufficient conditions are obtained such that encoder cooperation through the facilitator results in a gain in sum-capacity that has infinite slope in the information rate shared with the encoders. This result extends the prior work of the authors on cooperation in networks where none of the nodes have access to state information.
Zeros of the dilogarithm

We show that the dilogarithm has at most one zero on each branch, that each zero is close to a root of unity, and that they may be found to any precision with Newton's method. This work is motivated by applications to the asymptotics of coefficients in partial fraction decompositions considered by Rademacher. We also survey what is known about zeros of polylogarithms in general.
Multi-View Networks for Denoising of Arbitrary Numbers of Channels

We propose a set of denoising neural networks capable of operating on an arbitrary number of channels at runtime, irrespective of how many channels they were trained on. We coin the proposed models multi-view networks since they operate using multiple views of the same data. We explore two such architectures and show how they outperform traditional denoising models in multi-channel scenarios. Additionally, we demonstrate how multi-view networks can leverage information provided by additional recordings to make better predictions, and how they are able to generalize to a number of recordings not seen in training.
SYNDETIC SETS AND AMENABILITY

We prove that if an infinite, discrete semigroup has the property that every right syndetic set is left syndetic, then the semigroup has a left invariant mean. We prove that the weak*-closed convex hull of the two-sided translates of every bounded function on an infinite discrete semigroup contains a constant function. Our proofs use the algebraic properties of the Stone-Cech compactification. 1. The Main Theorems Let S be an infinite discrete semigroup. Given f 2 ` 1 (S) and t 2 S set (tf)(s) = f t (s) = f(st) and rt(f) = f t which is called the right translate of f by t. Similarly, we set (ft)(s) = ft(s) = f(ts) and lt(f) = ft which is called the left translate of f by t. Moreover, t ! tf and t ! ft define associative, left and right actions of S on ` 1 (S): A classic result of Mitchell(5) says that the weak*-closed convex hull of the set of right(respectively, left) translates of f contains a constant function for every f 2 ` 1 (S) if and only if ` 1 (S) has a left(respectively, right) invariant mean. A semigroup is called left(respectively, right) amenable if ` 1 (S) has a left(respectively, right) invariant mean. For a simpler proof of Mitchell's result, along with an extension to the topological case, see the paper of Granirer and Lau(3). M. M. Day proved(2) that if a semigroup has a left invariant mean and a right invariant mean, then it has a mean that is simultaneously left and right invariant, called an invariant mean.. A semigroup with an invariant mean is called amenable. By another result of Day(2), any group that has a left or right invariant mean has an invariant mean. However, Day also gave examples of semigroups that had left(respectively, right) invariant means but no right(respectively, left) invariant means. In these notes we prove the following theorems. Theorem 1. Let S be an infinite discrete semigroup, let f 2 ` 1 (S);and let C(f) denote the weak*-closed, convex hull of the set of functions obtained by taking right and left translates of f:Then C(f) contains a constant function.
Nested Critical Points for a Directed Polymer on a Disordered Diamond Lattice

We consider a model for a directed polymer in a random environment defined on a hierarchical diamond lattice in which i.i.d. random variables are attached to the lattice bonds. Our focus is on scaling schemes in which a size parameter n, counting the number of hierarchical layers of the system, becomes large as the inverse temperature $$\beta $$ vanishes. When $$\beta $$ has the form $${\widehat{\beta }}/\sqrt{n}$$ for a parameter $${\widehat{\beta }}>0$$ , we show that there is a cutoff value $$0< \kappa < \infty $$ such that as $$n \rightarrow \infty $$ the variance of the normalized partition function tends to zero for $${\widehat{\beta }}\le \kappa $$ and grows without bound for $${\widehat{\beta }}> \kappa $$ . We obtain a more refined description of the border between these two regimes by setting the inverse temperature to $$\kappa /\sqrt{n} + \alpha _n$$ where $$0 < \alpha _n \ll 1/\sqrt{n}$$ and analyzing the asymptotic behavior of the variance. We show that when $$\alpha _n = \alpha (\log n-\log \log n)/n^{3/2}$$ (with a small modification to deal with non-zero third moment), there is a similar cutoff value $$\eta $$ for the parameter $$\alpha $$ such that the variance goes to zero when $$\alpha < \eta $$ and grows without bound when $$\alpha > \eta $$ . Extending the analysis yet again by probing around the inverse temperature $$(\kappa / \sqrt{n}) + \eta (\log n-\log \log n)/n^{3/2}$$ , we find an infinite sequence of nested critical points for the variance behavior of the normalized partition function. In the subcritical cases $${\widehat{\beta }}\le \kappa $$ and $$\alpha \le \eta $$ , this analysis is extended to a central limit theorem result for the fluctuations of the normalized partition function.
The Existence of a Global Attractor for the Forced Critical Surface Quasi-Geostrophic Equation in \(L^2\)

We prove that the critical surface quasi-geostrophic equation driven by a force f possesses a compact global attractor in $$L^2(\mathbb T^2)$$ provided $$f\in L^p(\mathbb T^2)$$ for some $$p>2$$ . First, the De Giorgi method is used to obtain uniform $$L^\infty $$ estimates on viscosity solutions. Even though this does not provide a compact absorbing set, the existence of a compact global attractor follows from the continuity of solutions, which is obtained by estimating the energy flux using the Littlewood–Paley decomposition.
Geometrically nilpotent subvarieties

Abstract We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several related open questions are stated and discussed.
Learning to detect sepsis with a multitask Gaussian process RNN classifier

We present a scalable end-to-end classifier that uses streaming physiological and medication data to accurately predict the onset of sepsis, a life-threatening complication from infections that has high mortality and morbidity. Our proposed framework models the multivariate trajectories of continuous-valued physiological time series using multitask Gaussian processes, seamlessly accounting for the high uncertainty, frequent missingness, and irregular sampling rates typically associated with real clinical data. The Gaussian process is directly connected to a black-box classifier that predicts whether a patient will become septic, chosen in our case to be a recurrent neural network to account for the extreme variability in the length of patient encounters. We show how to scale the computations associated with the Gaussian process in a manner so that the entire system can be discriminatively trained end-to-end using backpropagation. In a large cohort of heterogeneous inpatient encounters at our university health system we find that it outperforms several baselines at predicting sepsis, and yields 19.4% and 55.5% improved areas under the Receiver Operating Characteristic and Precision Recall curves as compared to the NEWS score currently used by our hospital.
Collaborative Deep Learning for speech enhancement: A run-time model selection method using autoencoders

We show that a Modular Neural Network (MNN) can combine various speech enhancement modules, each of which is a Deep Neural Network (DNN) specialized on a particular enhancement job. Differently from an ordinary ensemble technique that averages variations in models, the propose MNN selects the best module for the unseen test signal to produce a greedy ensemble. We see this as Collaborative Deep Learning (CDL), because it can reuse various already-trained DNN models without any further refining. In the proposed MNN selecting the best module during run time is challenging. To this end, we employ a speech AutoEncoder (AE) as an arbitrator, whose input and output are trained to be as similar as possible if its input is clean speech. Therefore, the AE can gauge the quality of the module-specific denoised result by seeing its AE reconstruction error, e.g. low error means that the module output is similar to clean speech. We propose an MNN structure with various modules that are specialized on dealing with a specific noise type, gender, and input Signal-to-Noise Ratio (SNR) value, and empirically prove that it almost always works better than an arbitrarily chosen DNN module and sometimes as good as an oracle result.
L p -nondegenerate Radon-like operators with vanishing rotational curvature

We consider the $L^p \rightarrow L^q$ mapping properties of a model family of Radon-like operators integrating functions over n-dimensional submanifolds of ${\mathbb R}^{2n}$. It is shown that nonvanishing rotational curvature is never generic when $n \geq 2$ and is, in fact, impossible for all but finitely many values of $n$. Nevertheless, operators satisfying the same $L^p \rightarrow L^q$ estimates as the "nondegenerate" case (modulo the endpoint) are dense in the model family for all $n$.
Data-Efficient Minimax Quickest Change Detection With Composite Post-Change Distribution

The problem of quickest change detection is studied, where there is an additional constraint on the cost of observations used before the change point and where the post-change distribution is composite. Minimax formulations are proposed for this problem. It is assumed that the post-change family of distributions has a member which is least favorable in a well-defined sense. An algorithm is proposed in which ON–OFF observation control is employed using the least favorable distribution, and a generalized likelihood ratio-based approach is used for change detection. Under additional conditions on the post-change family of distributions, it is shown that the proposed algorithm is asymptotically optimal, uniformly for all possible post-change distributions.
Skewless network clock synchronization

This paper examines synchronization of computer clocks connected via a data network and proposes a skewless algorithm to synchronize them. Unlike existing solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, our algorithm achieves synchronization without these problems. We first analyze the convergence property of the algorithm and provide necessary and sufficient conditions on the parameters to guarantee synchronization. We then implement our solution on a cluster of IBM BladeCenter servers running Linux and study its performance. In particular, both analytically and experimentally, we show that our algorithm can converge in the presence of timing loops. This marks a clear contrast with current standards such as NTP and PTP, where timing loops are specifically avoided. Furthermore, timing loops can even be beneficial in our scheme. For example, it is demonstrated that highly connected subnetworks can collectively outperform individual clients when the time source has large jitter. It is also experimentally demonstrated that our algorithm outperforms other well-established software-based solutions such as the NTPv4 and IBM Coordinated Cluster Time (IBM CCT).
Effective action for the Abelian-Higgs model for a gauge-invariant implementation on optical lattices

We present a gauge-invariant effective action for the Abelian-Higgs model in 1+1 dimensions. It is constructed by integrating out the gauge field and then using the hopping parameter expansion. The latter is tested with Monte Carlo simulations for small values of the scalar self-coupling. In the opposite limit, at infinitely large self-coupling, the Higgs mode is frozen and the partition function can be written in terms of local tensors and the tensor renormalization group blocking can be applied. The numerical implementation requires truncations and the time continuum limit of the blocked transfer matrix can be obtained numerically. At zero gauge coupling and with a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large onsite repulsion. The procedure is extended to finite gauge coupling and we derive a spin-1 approximation of the Hamiltonian which involves terms corresponding to transitions among the two species in the Bose-Hubbard model. An optical lattice implementation involving a ladder structure is proposed.
Remarks on the Fractional Laplacian with Dirichlet Boundary Conditions and Applications

We prove nonlinear lower bounds and commutator estimates for the Dirichlet fractional Laplacian in bounded domains. The applications include bounds for linear drift-diffusion equations with nonlocal dissipation and global existence of weak solutions of critical surface quasi-geostrophic equations.
Extensions of Bernstein’s Lethargy Theorem

In this paper, we examine the aptly-named “Lethargy Theorem” of Bernstein and survey its recent extensions. We show that one of these extensions shrinks the interval for best approximation by half while the other gives a surprising connection to the space of bounded linear operators between two Banach spaces.
Higher index theory for certain expanders and Gromov monster groups, II

Abstract In this paper, the first of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs is an expander and the girth of the graphs tends to infinity, then the coarse Baum–Connes assembly map is injective, but not surjective, for the associated metric space X . Expanders with this girth property are a necessary ingredient in the construction of the so-called ‘Gromov monster’ groups that (coarsely) contain expanders in their Cayley graphs. We use this connection to show that the Baum–Connes assembly map with certain coefficients is injective but not surjective for these groups. Using the results of the second paper in this series, we also show that the maximal Baum–Connes assembly map with these coefficients is an isomorphism.
CLASSIFICATION OF CONGRUENCES FOR MOCK THETA FUNCTIONS AND WEAKLY HOLOMORPHIC MODULAR FORMS

Let $f(q)$ denote Ramanujan's mock theta function \[f(q) = \sum_{n=0}^{\infty} a(n) q^{n} := 1+\sum_{n=1}^{\infty} \frac{q^{n^{2}}}{(1+q)^{2}(1+q^{2})^{2}\cdots(1+q^{n})^{2}}.\] It is known that there are many linear congruences for the coefficients of $f(q)$ and other mock theta functions. We prove that if the linear congruence $a(mn+t) \equiv 0 \pmod{\ell}$ holds for some prime $\ell \geq 5$, then $\ell | m$ and $(\frac{24t-1}{\ell}) \neq (\frac{-1}{\ell})$. We prove analogous results for the mock theta function $\omega(q)$ and for a large class of weakly holomorphic modular forms which includes $\eta$-quotients. This extends work of Radu in which he proves a conjecture of Ahlgren and Ono for the partition function $p(n)$.
Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation

National Science Foundation [DMS-1217065, DMS-1418775, DMS-1419044]; U.S. Department of Energy [DE-AC02-05CH11231]; National Science Foundation
Going Deeper into First-Person Activity Recognition

We bring together ideas from recent work on feature design for egocentric action recognition under one framework by exploring the use of deep convolutional neural networks (CNN). Recent work has shown that features such as hand appearance, object attributes, local hand motion and camera ego-motion are important for characterizing first-person actions. To integrate these ideas under one framework, we propose a twin stream network architecture, where one stream analyzes appearance information and the other stream analyzes motion information. Our appearance stream encodes prior knowledge of the egocentric paradigm by explicitly training the network to segment hands and localize objects. By visualizing certain neuron activation of our network, we show that our proposed architecture naturally learns features that capture object attributes and hand-object configurations. Our extensive experiments on benchmark egocentric action datasets show that our deep architecture enables recognition rates that significantly outperform state-of-the-art techniques – an average 6:6% increase in accuracy over all datasets. Furthermore, by learning to recognize objects, actions and activities jointly, the performance of individual recognition tasks also increase by 30% (actions) and 14% (objects). We also include the results of extensive ablative analysis to highlight the importance of network design decisions.
Learning Model Predictive Control for Iterative Tasks: A Computationally Efficient Approach for Linear System

Abstract A Learning Model Predictive Controller (LMPC) for linear system is presented. The proposed controller builds on previous work on nonlinear LMPC and decreases its computational burden for linear system. The control scheme is reference-free and is able to improve its performance by learning from previous iterations. A convex safe set and a terminal cost function are used in order to guarantee recursive feasibility and non-increasing performance at each iteration. The paper presents the control design approach, and shows how to recursively construct the convex terminal set and the terminal cost from state and input trajectories of previous iterations. Simulation results show the effectiveness of the proposed control logic.
Relating Divisive Normalization to Neuronal Response Variability.

Cortical responses to repeated presentations of a sensory stimulus are variable. This variability is sensitive to several stimulus dimensions, suggesting that it may carry useful information beyond the average firing rate. Many experimental manipulations that affect response variability are also known to engage divisive normalization, a widespread operation that describes neuronal activity as the ratio of a numerator (representing the excitatory stimulus drive) and denominator (the normalization signal). Although it has been suggested that normalization affects response variability, we lack a quantitative framework to determine the relation between the two. Here we extend the standard normalization model, by treating the numerator and the normalization signal as variable quantities. The resulting model predicts a general stabilizing effect of normalization on neuronal responses, and allows us to infer the single-trial normalization strength, a quantity that cannot be measured directly. We test the model on neuronal responses to stimuli of varying contrast, recorded in primary visual cortex of male macaques. We find that neurons that are more strongly normalized fire more reliably, and response variability and pairwise noise correlations are reduced during trials in which normalization is inferred to be strong. Our results thus suggest a novel functional role for normalization, namely, modulating response variability. Our framework could enable a direct quantification of the impact of single-trial normalization strength on the accuracy of perceptual judgments, and can be readily applied to other sensory and nonsensory factors. SIGNIFICANCE STATEMENT Divisive normalization is a widespread neural operation across sensory and nonsensory brain areas, which describes neuronal responses as the ratio between the excitatory drive to the neuron and a normalization signal. Normalization plays a key role in several important computations, including adjusting the neuron9s dynamic range, reducing redundancy, and facilitating probabilistic inference. However, the relation between normalization and neuronal response variability (a fundamental aspect of neural coding) remains unclear. Here we develop a new model and test it on primary visual cortex responses. We show that normalization has a stabilizing effect on neuronal activity, beyond the known suppression of firing rate. This modulation of variability suggests a new functional role for normalization in neural coding and perception.
A Semismooth Predictor Corrector Method for Suboptimal Model Predictive Control

Suboptimal model predictive control is a technique that can reduce the computational cost of model predictive control (MPC) by exploiting its robustness to incomplete optimization. Instead of solving the optimal control problem exactly, this method maintains an estimate of the optimal solution and updates it at each sampling instance. The resulting controller can be viewed as a dynamic compensator which runs in parallel with the plant. This paper explores the use of the semismooth predictor-corrector method to implement suboptimal MPC. The dynamic interconnection of the combined plant-optimizer system is studied using the input-to-state stability framework and sufficient conditions for closed-loop asymptotic stability and constraint enforcement are derived using small gain arguments. Numerical simulations demonstrate the efficacy of the scheme.
Generalized designs on graphs: Sampling, spectra, symmetries

Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They are evenly distributed and often exhibit a great degree of regularity and symmetry. We point out that a spectral definition of spherical designs easily transfers to finite graphs -- these 'graphical designs' are subsets of vertices that are evenly spaced and capture the symmetries of the underlying graph (should they exist). Our main result states that good graphical designs either consist of many vertices or their neighborhoods have exponential volume growth. We show several examples, describe ways to find them and discuss problems.
Multi-class twitter data categorization and geocoding with a novel computing framework

Abstract This study details the progress in transportation data analysis with a novel computing framework in keeping with the continuous evolution of the computing technology. The computing framework combines the Labeled Latent Dirichlet Allocation (L-LDA)-incorporated Support Vector Machine (SVM) classifier with the supporting computing strategy on publicly available Twitter data in determining transportation-related events to provide reliable information to travelers. The analytical approach includes analyzing tweets using text classification and geocoding locations based on string similarity. A case study conducted for the New York City and its surrounding areas demonstrates the feasibility of the analytical approach. Approximately 700,010 tweets are analyzed to extract relevant transportation-related information for one week. The SVM classifier achieves >85% accuracy in identifying transportation-related tweets from structured data. To further categorize the transportation-related tweets into sub-classes: incident, congestion, construction, special events, and other events, three supervised classifiers are used: L-LDA, SVM, and L-LDA incorporated SVM. Findings from this study demonstrate that the analytical framework, which uses the L-LDA incorporated SVM, can classify roadway transportation-related data from Twitter with over 98.3% accuracy, which is significantly higher than the accuracies achieved by standalone L-LDA and SVM.
Explicit Polar Codes with Small Scaling Exponent

Polar coding gives rise to the first explicit family of codes that provably achieve capacity for a wide range of channels with efficient encoding and decoding. But how fast can polar coding approach capacity as a function of the code length? In finite-length analysis, the scaling between code length and the gap to capacity is usually measured in terms of the scaling exponent µ. It is well known that the optimal scaling exponent, achieved by random binary codes, is µ = 2. It is also well known that the scaling exponent of conventional polar codes on the binary erasure channel (BEC) is µ = 3.627, which falls far short of the optimal value. On the other hand, it was recently shown that polar codes derived from l × l binary polarization kernels approach the optimal scaling exponent µ = 2 on the BEC as l→∞, with high probability over a random choice of the kernel.Herein, we focus on explicit constructions of l×l binary kernels with small scaling exponent for l ⩽ 64. In particular, we exhibit a sequence of binary linear codes that approaches capacity on the BEC with quasi-linear complexity and scaling exponent µ l transforms an underlying BEC into l bit-channels W 1 , W 2 ,…, W l . The erasure probabilities of W 1 , W 2 ,…, W l , known as the polarization behavior of K l , determine the resulting scaling exponent µ(K l ). We first introduce a class of self-dual binary kernels and prove that their polarization behavior satisfies a strong symmetry property. This reduces the problem of constructing K l to that of producing a certain nested chain of only l/2 self-orthogonal codes. We use nested cyclic codes, whose distance is as high as possible subject to the orthogonality constraint, to construct the kernels K 32 and K 64 . In order to evaluate the polarization behavior of K 32 and K 64 , two alternative trellis representations (which may be of independent interest) are proposed. Using the resulting trellises, we show that µ(K 32 ) = 3.122 and explicitly compute over half of the polarization-behavior coefficients for K 64 , at which point the complexity becomes prohibitive. To complete the computation, we introduce a Monte-Carlo interpolation method, which produces the estimate µ(K 64 ) ≃ 2.87. We augment this estimate with a rigorous proof that µ(K 64 ) < 2.97.
Uncertainty Guided Semi-supervised Segmentation of Retinal Layers in OCT Images

Deep convolutional neural networks have shown outstanding performance in medical image segmentation tasks. The usual problem when training supervised deep learning methods is the lack of labeled data which is time-consuming and costly to obtain. In this paper, we propose a novel uncertainty guided semi-supervised learning based on student-teacher approach for training the segmentation network using limited labeled samples and large number of unlabeled images. First, a teacher segmentation model is trained from the labeled samples using Bayesian deep learning. The trained model is used to generate soft segmentation labels and uncertainty map for the unlabeled set. The student model is then updated using the softly segmented samples and the corresponding pixel-wise confidence of the segmentation quality estimated from the uncertainty of the teacher model using a newly designed loss function. Experimental results on a retinal layer segmentation task show that the proposed method improves the segmentation performance in comparison to the fully supervised approach and is on par with the expert annotator. The proposed semi-supervised segmentation framework is a key contribution and applicable for biomedical image segmentation across various imaging modalities where access to annotated medical images is challenging.
WiFi Motion Detection: A Study into Efficacy and Classification

WiFi and security pose both an issue and act as a growing presence in everyday life. Today’s motion detection implementations are severely lacking in the areas of secrecy, scope, and cost. To combat this problem, we aim to develop a motion detection system that utilizes WiFi Channel State Information (CSI), which describes how a wireless signal propagates from the transmitter to the receiver. The goal of this study is to develop a real-time motion detection and classification system that is discreet, cost-effective, and easily implementable. The system would only require an Ubuntu laptop with an Intel Ultimate N WiFi Link 5300 and a standard router. The system will be developed in two parts: (1) a robust system to track CSI variations in real-time, and (2) an algorithm to classify the motion. The system used to track CSI variance in real-time was completed in August 2018. Initial results show that introduction of motion to a previously motionless area is detected with high confidence. We present the development of (1) anomaly detection, utilizing the moving average filter implemented in the initial program and/or unsupervised machine learning, and (2) supervised machine learning algorithms to classify a set of simple motions using a proposed feature extraction methods. Lastly, classification methods such as Decision Tree, Naive Bayes, and Long Short-Term Memory can be used to classify basic actions regardless of speed, location, or orientation.
A look at jobless recoveries in G7 countries

Abstract We study changes in the plucking behavior of employment growth, as well as changes in its relationship with the output cycle in the G7 countries. Using both revised and real-time data, we consider several popular measures of the output cycle. For most countries, we see significant evidence in favor of structural changes in the response coefficients of employment growth to its own gap, suggesting much slower recoveries in labor markets, consistent with the jobless recoveries hypothesis. However, we also find evidence in favor of heterogeneity across countries, both in the responses of employment to employment gaps and in the responses of employment to the output cycle.
Gamma ray astrophysics

Gamma ray production processes are reviewed, including Compton scattering, synchrotron radiation, bremsstrahlung interactions, meson decay, nucleon-antinucleon annihilations, and pion production. Gamma ray absorption mechanisms through interactions with radiation and with matter are discussed, along with redshifts and gamma ray fluxes.