cssi/SciSciGPT-SciSciNet huggingface dataset:
Trends in Characteristics, Mortality, and Other Outcomes of Patients With Newly Diagnosed Cirrhosis.

Importance Changes in the characteristics of patients with cirrhosis are likely to affect future outcomes and are important to understand in planning for the care of this population. Objective To identify changes in demographic and clinical characteristics and outcomes in patients with newly diagnosed cirrhosis. Design, Setting, and Participants A retrospective cohort study of patients with a new diagnosis of cirrhosis was conducted using the Indiana Network for Patient Care, a large statewide regional health information exchange, between 2004 and 2014. Patients with at least 1 year of continuous follow-up before the cirrhosis diagnosis were followed up through August 1, 2015. The analysis was conducted from December 2018 to January 2019. Exposures Age, cause of cirrhosis, and year of diagnosis. Main Outcomes and Measures Overall rates for mortality, liver transplant, hepatocellular carcinoma, and hepatic decompensation (composite of ascites, hepatic encephalopathy, or variceal bleeding). Results A total of 9261 patients with newly diagnosed cirrhosis were identified (mean [SD] age, 57.9 [12.6] years; 5109 [55.2%] male). A 69% increase in new diagnoses occurred over the course of the study period (620 in 2004 vs 1045 in 2014). The proportion of those younger than 40 years increased by 0.20% per year (95% CI, 0.04% to 0.36%;Pfor trend = .02), and the proportion of those aged 65 years and older increased by 0.81% per year (95% CI, 0.51% to 1.11%;Pfor trend Conclusions and Relevance The population of patients with newly diagnosed cirrhosis in Indiana has experienced changes in the age distribution and cause of cirrhosis, with decreasing mortality rates. These findings support investment in the prevention and treatment of alcoholic liver disease and nonalcoholic steatohepatitis, particularly in younger and older patients. Additional study is needed to identify the reasons for decreasing mortality rates.
Comparison and pure infiniteness of crossed products

Let $\alpha: G\curvearrowright X$ be a continuous action of an infinite countable group on a compact Hausdorff space. We show that, under the hypothesis that the action $\alpha$ is topologically free and has no $G$-invariant regular Borel probability measure on $X$, dynamical comparison implies that the reduced crossed product of $\alpha$ is purely infinite and simple. This result, as an application, shows a dichotomy between stable finiteness and pure infiniteness for reduced crossed products arising from actions satisfying dynamical comparison. We also introduce the concepts of paradoxical comparison and the uniform tower property. Under the hypothesis that the action $\alpha$ is exact and essentially free, we show that paradoxical comparison together with the uniform tower property implies that the reduced crossed product of $\alpha$ is purely infinite. As applications, we provide new results on pure infiniteness of reduced crossed products in which the underlying spaces are not necessarily zero-dimensional. Finally, we study the type semigroups of actions on the Cantor set in order to establish the equivalence of almost unperforation of the type semigroup and comparison. This sheds a light to a question arising in the paper of R{\o}rdam and Sierakowski.
Hyperparathyroidism and parathyroidectomy in X-linked hypophosphatemia patients.

Abstract Background X-linked hypophosphatemia (XLH) causes rickets, osteomalacia, skeletal deformities and growth impairment, due to elevated fibroblast growth factor 23 and hypophosphatemia. Conventional therapy requires high doses of phosphate salts combined with active vitamin D analogues. Risks of this regimen include nephrocalcinosis and secondary hyperparathyroidism or progression to tertiary (hypercalcemic) hyperparathyroidism. Methods The primary goals were to estimate the prevalence of hyperparathyroidism and to characterize parathyroidectomy outcomes regarding hypercalcemia among XLH patients. XLH patients attending our center from 1/2000 to 12/2017 were included in a retrospective chart review. Prevalence of nephrocalcinosis and eGFR Results Of 104 patients with XLH, 84 had concurrent measurements of calcium and PTH (40 adults and 44 children). Of these, 70/84 (83.3%), had secondary or tertiary hyperparathyroidism at any time point. Secondary hyperparathyroidism was persistent in 62.2% of those with data at multiple timepoints. Tertiary hyperparathyroidism had an overall prevalence of 14/84 (16.7%) patients. Parathyroidectomy was performed in 8/84 (9.5%) of the total population. After parathyroidectomy, persistent or recurrent tertiary hyperparathyroidism was detected in 6/8 (75%) patients at a median of 6 years (from 0 to 29 years). One patient had chronic post-surgical hypoparathyroidism and one patient remained normocalcemic 4 years after surgery. Nephrocalcinosis was more prevalent in patients with tertiary hyperparathyroidism than those without (60.0% vs 18.6%). Chronic kidney disease (eGFR Conclusion The majority of patients with XLH develop secondary hyperparathyroidism during treatment with phosphate and active vitamin D. A significant proportion develops tertiary hyperparathyroidism and most have recurrence or persistence of hypercalcemia after surgery.
Cerebellar disruption impairs working memory during evidence accumulation

To select actions based on sensory evidence, animals must create and manipulate representations of stimulus information in memory. Here we report that during accumulation of somatosensory evidence, optogenetic manipulation of cerebellar Purkinje cells reduces the accuracy of subsequent memory-guided decisions and causes mice to downweight prior information. Behavioral deficits are consistent with the addition of noise and leak to the evidence accumulation process. We conclude that the cerebellum can influence the accurate maintenance of working memory.
A 130 GeV gamma ray signal from supersymmetry

Abstract The viability of neutralino dark matter as an explanation of the 130 GeV gamma ray signal from the Galactic Center recently observed by the Fermi Large Area Telescope is examined. It is found that the signal can be compatible with a sharp feature from internal bremsstrahlung from a mostly bino dark matter particle of mass around 145 GeV, augmented by a contribution from annihilation into gamma+Z via a small wino admixture. This scenario circumvents the problematic overproduction of lower energy continuum photons that plague line interpretations of this signal. Sleptons approximately degenerate in mass with the neutralino are required to enhance the internal bremsstrahlung feature.
Leveraging One-Hop Information in Massive MIMO Full-Duplex Wireless Systems

We consider a single-cell massive multiple input multiple output full-duplex wireless communication system, where the base-station (BS) is equipped with a large number of antennas. We consider the setup where the single-antenna mobile users operate in half-duplex, while each antenna at the BS is capable of full-duplex transmissions, i.e., it can transmit and receive simultaneously using the same frequency spectrum. The fundamental challenge in this system is intra-cell inter-node interference, generated by the transmissions of uplink users to the receptions at the downlink users. The key operational challenge is estimating and aggregating inter-mobile channel estimates, which can potentially overwhelm any gains from full-duplex operation. In this paper, we propose a scalable and distributed scheme to optimally manage the inter-node interference by utilizing a “one-hop information architecture” . In this architecture, the BS only needs to know the signal-to-interference-plus-noise ratio from the downlink users. Each uplink user needs its own SINR, along with a weighted signal-plus-noise metric from its one-hop neighboring downlink users, which are the downlink users, that it interferes with. The proposed one-hop information architecture does not require any network devices to comprehensively gather the vast inter-node interference channel knowledge, and hence significantly reduces the overhead. Based on the one-hop information architecture, we design a distributed power control algorithm and implement such architecture using overheard feedback information. We show that, in typical asymptotic regimes with many users and antennas, the proposed distributed power control scheme improves the overall network utility and reduces the transmission power of the uplink users.
Global existence for the multi-dimensional compressible viscoelastic flows

Abstract The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces. Using uniform estimates for a hyperbolic–parabolic linear system with convection terms, we prove the global existence in the Besov space which is invariant with respect to the scaling of the associated equations. Several important estimates are achieved, including a smoothing effect on the velocity, and the L 1 -decay of the density and deformation gradient.
Congestion barcodes: Exploring the topology of urban congestion using persistent homology

This work presents a new method to quantify connectivity in transportation networks. Inspired by the field of topological data analysis, we propose a novel approach to explore the robustness of road network connectivity in the presence of congestion on the roadway. The robustness of the pattern is summarized in a congestion barcode, which can be constructed directly from traffic datasets commonly used for navigation. As an initial demonstration, we illustrate the main technique on a publicly available traffic dataset in a neighborhood in New York City.
Proof of an entropy conjecture of Leighton and Moitra

Abstract We prove the following conjecture of Leighton and Moitra. Let T be a tournament on [ n ] and S n the set of permutations of [ n ] . For an arc uv of T, let A u v = { σ ∈ S n : σ ( u ) σ ( v ) } . Theorem For a fixed e > 0 , if P is a probability distribution on S n such that P ( A u v ) > 1 / 2 + e for every arc uv of T, then the binary entropy of P is at most ( 1 − ϑ e ) log 2 ⁡ n ! for some (fixed) positive ϑ e . When T is transitive the theorem is due to Leighton and Moitra; for this case we give a short proof with a better ϑ e .
Light forces in ultracold photoassociation

We study the time-resolved photoassociation of ultracold sodium in an optical dipole trap. The photoassociation laser excites pairs of atoms to molecular states of large total angular momentum at high intensities (above $20\phantom{\rule{0.3em}{0ex}}\mathrm{kW}∕{\mathrm{cm}}^{2}$). Such transitions are generally suppressed at ultracold temperatures by the centrifugal barriers for high partial waves. Time-resolved ionization measurements reveal that the atoms are accelerated by the dipole potential of the photoassociation beam. We change the collision energy by varying the potential depth, and observe a strong variation of the photoassociation rate. These results demonstrate the important role of light forces in cw photoassociation at high intensities.
Endpoint bounds of square functions associated with Hankel multipliers

We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on L radial functions. This is a consequence of endpoint bounds for a corresponding square function for Hankel multipliers. We obtain a sharp Marcinkiewicz-type multiplier theorem for multivariate Hankel multipliers and L bounds of maximal operators generated by Hankel multipliers as corollaries. The proof is built on techniques developed by Garrigos and Seeger for characterizations of Hankel multipliers.
The assistive multi-armed bandit

Learning preferences implicit in the choices humans make is a well studied problem in both economics and computer science. However, most work makes the assumption that humans are acting (noisily) optimally with respect to their preferences. Such approaches can fail when people are themselves learning about what they want. In this work, we introduce the assistive multi-armed bandit, where a robot assists a human playing a bandit task to maximize cumulative reward. In this problem, the human does not know the reward function but can learn it through the rewards received from arm pulls; the robot only observes which arms the human pulls but not the reward associated with each pull. We offer sufficient and necessary conditions for successfully assisting the human in this framework. Surprisingly, better human performance in isolation does not necessarily lead to better performance when assisted by the robot: a human policy can do better by effectively communicating its observed rewards to the robot. We conduct proof-of-concept experiments that support these results. We see this work as contributing towards a theory behind algorithms for human-robot interaction.
Shifted lattices and asymptotically optimal ellipses

Translate the positive-integer lattice points in the first quadrant by some amount in the horizontal and vertical directions, and consider a decreasing concave (or convex) curve in the first quadrant. Construct a family of curves by rescaling in the coordinate directions while preserving area, and identify the curve in the family that encloses the greatest number of the shifted lattice points. We find the limiting shape of this maximizing curve as the area is scaled up towards infinity. The limiting shape depends explicitly on the lattice shift, except that when the shift is too negative, the maximizing curve fails to converge and instead degenerates. Our results handle the p-circle $$x^p+y^p=1$$ when $$p>1$$ (concave) and also when $$0<p<1$$ (convex). The circular case $$p=2$$ with shift $$-1/2$$ corresponds to minimizing high eigenvalues in a symmetry class for the Laplacian on rectangles, while the straight line case ( $$p=1$$ ) generates an open problem about minimizing high eigenvalues of quantum harmonic oscillators with normalized parabolic potentials.
Photodetector figures of merit in terms of POVMs

A photodetector may be characterized by various figures of merit such as response time, bandwidth, dark count rate, efficiency, wavelength resolution, and photon-number resolution. On the other hand, quantum theory says that any measurement device is fully described by its positive-operator-valued measure (POVM) which generalizes the textbook notion of the eigenstates of the appropriate hermitian operator (the 'observable') as measurement outcomes. Here we show how to define a multitude of photodetector figures of merit in terms of a given POVM. We distinguish classical and quantum figures of merit and issue a conjecture regarding trade-off relations between them. We discuss the relationship between POVM elements and photodetector clicks, and how models of photodetectors may be tested by measuring either POVM elements or figures of merit. Finally, the POVM is advertised as a platform-independent way of comparing different types of photodetectors, since any such POVM refers to the Hilbert space of the incoming light, and not to any Hilbert space internal to the detector.
Multiplicity one theorem for the Ginzburg–Rallis model: The tempered case

Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove the multiplicity one theorem for the Ginzburg-Rallis model over the Vogan packets in the tempered case. In some cases, we can also relate the multiplicity to the epsilon factor. This is a sequel of our work \cite{Wan15} in which we consider the supercuspidal case.
Multilevel Diversity Coding Systems: Rate Regions, Codes, Computation, & Forbidden Minors

The rate regions of multilevel diversity coding systems (MDCSs), a sub-class of the broader family of multi-source multi-sink networks with special structure, are investigated in a systematic way. We enumerate all non-isomorphic MDCS instances with at most three sources and four encoders. Then, the exact rate region of every one of these more than 7000 instances is proven via computations showing that the Shannon outer bound matches with a custom constructed linear code-based inner bound. Results gained from these computations are summarized in key statistics involving aspects, such as the sufficiency of scalar binary codes, the necessary size of vector binary codes, and so on. Also, it is shown how to construct the codes for an achievability proof. Based on this large repository of rate regions, a series of results about general MDCS cases of arbitrary size that they inspired is introduced and proved. In particular, a series of embedding operations that preserve the property of sufficiency of scalar or vector codes is presented. The utility of these operations is demonstrated by boiling the thousands of MDCS instances for which scalar binary (superposition) codes are insufficient down to 12 (26) forbidden the smallest embedded MDCS instances.
Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces

In this paper we show that totally geodesic subspaces determine the commensurability class of a standard arithmetic hyperbolic $n$-orbifold, $n\ge 4$. Many of the results are more general and apply to locally symmetric spaces associated to arithmetic lattices in $\mathbb{R}$-simple Lie groups of type $B_n$ and $D_n$. We use a combination of techniques from algebraic groups and quadratic forms to prove several results about these spaces.
Strategic Coalitions with Perfect Recall

The paper proposes a bimodal logic that describes an interplay between distributed knowledge modality and coalition know-how modality. Unlike other similar systems, the one proposed here assumes perfect recall by all agents. Perfect recall is captured in the system by a single axiom. The main technical results are the soundness and the completeness theorems for the proposed logical system.
Order and disorder in SU(N) simplex solid antiferromagnets

We study the structure of quantum ground states of simplex solid models, which are generalizations of the valence bond construction for quantum antiferromagnets originally proposed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) (1987 Phys. Rev. Lett. 59 799). Whereas the AKLT states are created by application of bond singlet operators for spins, the simplex solid construction is based on N-simplex singlet operators for spins. In both cases, a discrete one-parameter family of translationally-invariant models with exactly solvable ground states is defined on any regular lattice, and the equal time ground state correlations are given by the finite temperature correlations of an associated classical model on the same lattice, owing to the product form of the wave functions when expressed in a coherent state representation. We study these classical companion models via a mix of Monte Carlo simulations, mean-field arguments, and low-temperature effective field theories. Our analysis reveals that the ground states of edge- and face-sharing cubic lattice simplex solid models are long range ordered for sufficiently large values of the discrete parameter, whereas the ground states of the models on the kagome (2D) and hyperkagome (3D) lattices are always quantum disordered. The kagome simplex solid exhibits strong local order absent in its three-dimensional hyperkagome counterpart, a contrast that we rationalize with arguments similar to those leading to 'order by disorder'.
Some trace inequalities for exponential and logarithmic functions

Consider a function F(X, Y) of pairs of positive matrices with values in the positive matrices such that whenever X and Y commute $$F(X,Y)= X^pY^q.$$ Our first main result gives conditions on F such that $$\mathrm{Tr}[ X \log (F(Z,Y))] \le \mathrm{Tr}[X(p\log X + q \log Y)]$$ for all X, Y, Z such that $$\mathrm{Tr}Z =\mathrm{Tr}X$$ . (Note that Z is absent from the right side of the inequality.) We give several examples of functions F to which the theorem applies. Our theorem allows us to give simple proofs of the well known logarithmic inequalities of Hiai and Petz and several new generalizations of them which involve three variables X, Y, Z instead of just X, Y alone. The investigation of these logarithmic inequalities is closely connected with three quantum relative entropy functionals: The standard Umegaki quantum relative entropy $$D(X||Y) = \mathrm{Tr}[X(\log X-\log Y])$$ , and two others, the Donald relative entropy $$D_D(X||Y)$$ , and the Belavkin–Stasewski relative entropy $$D_{BS}(X||Y)$$ . They are known to satisfy $$D_D(X||Y) \le D(X||Y)\le D_{BS}(X||Y)$$ . We prove that the Donald relative entropy provides the sharp upper bound, independent of Z on $$\mathrm{Tr}[ X \log (F(Z,Y))]$$ in a number of cases in which F(Z, Y) is homogeneous of degree 1 in Z and −1 in Y. We also investigate the Legendre transforms in X of $$D_D(X||Y)$$ and $$D_{BS}(X||Y)$$ , and show how our results about these Legendre transforms lead to new refinements of the Golden–Thompson inequality.
Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit

Abstract The Jordan type of a nilpotent matrix is the partition giving the sizes of its Jordan blocks. We study pairs of partitions ( P , Q ) , where Q = Q ( P ) is the Jordan type of a generic nilpotent matrix A commuting with a nilpotent matrix B of Jordan type P. T. Kosir and P. Oblak have shown that Q has parts that differ pairwise by at least two. Such partitions, which are also known as “super distinct” or “Rogers–Ramanujan”, are exactly those that are stable or “self-large” in the sense that Q ( Q ) = Q . In 2012 P. Oblak formulated a conjecture concerning the cardinality of Q − 1 ( Q ) when Q has two parts, and proved some special cases. R. Zhao refined this to posit that the partitions in Q − 1 ( Q ) for Q = ( u , u − r ) with u > r > 1 could be arranged in an ( r − 1 ) × ( u − r ) table T ( Q ) where the entry in the k-th row and l-th column has k + l parts. We prove this Table Theorem, and then generalize the statement to propose a Box Conjecture for the set of partitions Q − 1 ( Q ) for an arbitrary partition Q whose parts differ pairwise by at least two.
Density of polynomials in sub-Bergman Hilbert spaces

Abstract The sub-Bergman Hilbert spaces are analogues of de Branges–Rovnyak spaces in the Bergman space setting. We prove that the polynomials are dense in sub-Bergman Hilbert spaces. This answers the question posted by Zhu in the affirmative.
On fluctuations for random band Toeplitz matrices

In this paper, we study two one-parameter families of random band Toeplitz matrices: where (1) a0 = 0, {a1, a2, …} in An(t) are independent random variables and a-i = ai; (2) a0(t) = 0, {a1(t), a2(t), …} in Bn(t) are independent copies of the standard Brownian motion at time t and a-i(t) = ai(t). As t varies, the empirical measures μ(An(t)) and μ(Bn(t)) are measure valued stochastic processes. The purpose of this paper is to study the fluctuations of μ(An(t)) and μ(Bn(t)) as n goes to ∞. Given a monomial f(x) = xp with p ≥ 2, the corresponding rescaled fluctuations of μ(An(t)) and μ(Bn(t)) are respectively. We will prove that the above equations converge to centered Gaussian families {Zp(t)} and {Wp(t)} respectively. The covariance structure &#x1d53c;[Zp(t1)Zq(t2)] and &#x1d53c;[Wp(t1)Wq(t2)] are obtained for all p, q ≥ 2, t1, t2 ≥ 0, and are both homogeneous polynomials of t1 and t2 for fixed p, q. In particular, Z2(t) is the Brownian motion and Z3(t) is the same as W2(t) up to a constant. The main method of this paper is the moment method.
Existence of complete Kähler Ricci-flat metrics on crepant resolutions

In this note, we obtain existence results for complete Ricci-flat Kahler metrics on crepant resolutions of singularities of Calabi–Yau varieties. Furthermore, for certain asymptotically flat Calabi–Yau varieties, we show that the Ricci-flat metric on the resolved manifold has the same asymptotic behavior as the initial variety.
Resolutions for twisted tensor products

We build resolutions for general twisted tensor products of algebras. These bimodule and module resolutions unify many constructions in the literature and are suitable for computing Hochschild (co)homology and more generally Ext and Tor for (bi)modules. We analyze in detail the case of Ore extensions, consequently obtaining Chevalley-Eilenberg resolutions for universal enveloping algebras of Lie algebras (defining the cohomology of Lie groups and Lie algebras). Other examples include semidirect products, crossed products, Weyl algebras, Sridharan enveloping algebras, and Koszul pairs.
A second order local minimality criterion for the triple junction singularity of the Mumford-Shah functional

This paper is the first part of an ongoing project aimed at providing a local minimality criterion, based on a second variation approach, for the triple point configurations of the Mumford-Shah functional.
Meta-Learning Update Rules for Unsupervised Representation Learning

A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this involves minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations useful for subsequent tasks will arise as a side effect. In this work, we propose instead to directly target later desired tasks by meta-learning an unsupervised learning rule which leads to representations useful for those tasks. Specifically, we target semi-supervised classification performance, and we meta-learn an algorithm -- an unsupervised weight update rule -- that produces representations useful for this task. Additionally, we constrain our unsupervised update rule to a be a biologically-motivated, neuron-local function, which enables it to generalize to different neural network architectures, datasets, and data modalities. We show that the meta-learned update rule produces useful features and sometimes outperforms existing unsupervised learning techniques. We further show that the meta-learned unsupervised update rule generalizes to train networks with different widths, depths, and nonlinearities. It also generalizes to train on data with randomly permuted input dimensions and even generalizes from image datasets to a text task.
Exclusive Sparsity Norm Minimization With Random Groups via Cone Projection

Many practical applications such as gene expression analysis, multitask learning, image recognition, signal processing, and medical data analysis pursue a sparse solution for the feature selection purpose and particularly favor the nonzeros evenly distributed in different groups. The exclusive sparsity norm has been widely used to serve to this purpose. However, it still lacks systematical studies for exclusive sparsity norm optimization. This paper offers two main contributions from the optimization perspective: 1) we provide several efficient algorithms to solve exclusive sparsity norm minimization with either smooth loss or hinge loss (nonsmooth loss). All algorithms achieve the optimal convergence rate $O(1/k^{2})$ . ( $k$ is the iteration number.) To the best of our knowledge, this is the first time to guarantee such convergence rate for the general exclusive sparsity norm minimization and 2) when the group information is unavailable to define the exclusive sparsity norm, we propose to use the random grouping scheme to construct groups and prove that if the number of groups is appropriately chosen, the nonzeros (true features) would be grouped in the ideal way with high probability. Empirical studies validate the efficiency of the proposed algorithms, and the effectiveness of random grouping scheme on the proposed exclusive support vector machine formulation.
Persistent homology and Euler integral transforms

The Euler calculus—an integral calculus based on Euler characteristic as a valuation on constructible functions—is shown to be an incisive tool for answering questions about injectivity and invertibility of recent transforms based on persistent homology for shape characterization.
Chern-Simons inflation and baryogenesis

We present a model of inflation based on the interaction between a homogeneous and isotropic configuration of a U(1) gauge field and fermionic charge density 0. The regulated fermionic charge density is generated from a Bunch-Davies vacuum state using the methods of Koksma and Prokopec [11], and is found to redshift as 1/a(η). The time-like component of gauge field is sourced by the fermionic charge leading to a growth in the gauge field A(η)0 ~ a(η). As a result inflation is dominated by the energy density contained in the gauge field and fermionic charge interaction, A0 0, which remains constant during inflation. We also provide a mechanism to generate a net lepton asymmetry. The coupling of a pseudo scalar to the Chern-Simons term converts the gauge field fluctuations into lepton number and all three Sahkarov conditions are satisfied during inflation. Finally, the rapid oscillation of the pseudo scalar field near its minimum thermalizes the gauge field and ends inflation. We provide the necessary initial condition on the gauge field and fermionic charge to simultaneously generate enough e-folds and baryon asymmetry index.
Interpolation and Commutant Lifting with Weights

Our two principle goals are generalizations of the commutant lifting theorem and the Nevanlinna-Pick interpolation theorem to the context of Hardy algebras built from \(W^*\)-correspondences endowed with a sequence of weights. These theorems generalize theorems of Muhly and Solel from 1998 and 2004, respectively, which were proved in settings without weights. Of special interest is the fact that commutant lifting in our setting is a consequence of Parrott’s Lemma; it is inspired by work of Arias.
A Parking Function Bijection supporting the Haglund–Morse–Zabrocki Conjectures

The shuffle conjecture expresses a relationship between parking functions, diagonal harmonics, and the Bergeron-Garsia $\nabla$ operator. Recent conjectures about a family of modified Hall-Littlewood operators made by Haglund, Morse, and Zabrocki sharpen the shuffle conjecture and suggest a variety of combinatorial properties of parking functions. In particular, their conjectures combined with previously established commutativity laws of the Hall-Littlewood operators, suggest the existence of certain bijections relating parking functions with different diagonal compositions. In this paper we formulate a conjecture which yields an algorithm for the construction of these bijections, prove a special case, and give some applications.
Energy-Based Modulation for Noncoherent Massive SIMO Systems

An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. We propose a single-shot noncoherent scheme which does not use the instantaneous channel state information (CSI), but rather only the knowledge of the channel statistics, a transmitter that modulates information only in the amplitude of the symbols, and a receiver which measures only the average received energy across the antennas. This system model is motivated by the simplicity of the circuit design and the energy efficiency it entails for both the transmitter and the receiver. We propose constellation designs which are asymptotically optimal with respect to symbol error rate (SER) with an increasing number of antennas, for any finite signal-to-noise power ratio (SNR), under different assumptions on the availability of CSI statistics. We describe in detail the case when there is a bounded uncertainty on the moments of the fading distribution. We present the numerical results on the SER performance achieved by these designs and find that they outperform the existing amplitude-modulation-based noncoherent scheme of amplitude shift keying (ASK). They also achieve a smaller peak-to-average power ratio (PAPR) for scenarios with a low SNR or a large line-of-sight (LOS) component.
Qualitative Stability of Nonlinear Networked Systems

In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This technical note extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.
Learning Deep Disentangled Embeddings With the F-Statistic Loss

Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We combine these two active but independent lines of research and propose a new paradigm suitable for both goals. We propose and evaluate a novel loss function based on the $F$ statistic, which describes the separation of two or more distributions. By ensuring that distinct classes are well separated on a subset of embedding dimensions, we obtain embeddings that are useful for few-shot learning. By not requiring separation on all dimensions, we encourage the discovery of disentangled representations. Our embedding method matches or beats state-of-the-art, as evaluated by performance on recall@$k$ and few-shot learning tasks. Our method also obtains performance superior to a variety of alternatives on disentangling, as evaluated by two key properties of a disentangled representation: modularity and explicitness. The goal of our work is to obtain more interpretable, manipulable, and generalizable deep representations of concepts and categories.
Link invariants from finite racks

We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.
Model updating using sum of squares (SOS) optimization to minimize modal dynamic residuals

This research studies finite element (FE) model updating through sum of squares (SOS) optimization to minimize modal dynamic residuals. In the past few decades, many FE model updating algorithms have been studied to improve the similitude between a numerical model and the as-built structure. FE model updating usually requires solving nonconvex optimization problems, while most off-the-shelf optimization solvers can only find local optima. To improve the model updating performance, this paper proposes the SOS global optimization method for minimizing modal dynamic residuals of the generalized eigenvalue equations in structural dynamics. The proposed method is validated through both numerical simulation and experimental study of a four-story shear frame structure.
User Scheduling for Millimeter Wave MIMO Communications with Low-Resolution ADCs

In millimeter wave (mmWave) systems, we investigate uplink user scheduling when a basestation employs low-resolution analog-to-digital converters (ADCs) with a large number of antennas. To reduce power consumption in the receiver, low-resolution ADCs can be a potential solution for mmWave systems in which many antennas are likely to be deployed to compensate for the large path loss. Due to quantization error, we show that the channel structure in the beamspace, in addition to the channel magnitude and beamspace orthogonality, plays a key role in maximizing the achievable rates of scheduled users. Consequently, we derive the optimal criteria with respect to the channel structure in the beamspace that maximizes the uplink sum rate for multi- user multiple input multiple output (MIMO) systems with a zero-forcing receiver. Leveraging the derived criteria, we propose an efficient scheduling algorithm for mmWave systems with low-resolution ADCs. Numerical results validate that the proposed algorithm outperforms conventional user scheduling methods in terms of the sum rate.
Submatrix localization via message passing

The principal submatrix localization problem deals with recovering a $K\times K$ principal submatrix of elevated mean $\mu$ in a large $n\times n$ symmetric matrix subject to additive standard Gaussian noise. This problem serves as a prototypical example for community detection, in which the community corresponds to the support of the submatrix. The main result of this paper is that in the regime $\Omega(\sqrt{n}) \leq K \leq o(n)$, the support of the submatrix can be weakly recovered (with $o(K)$ misclassification errors on average) by an optimized message passing algorithm if $\lambda = \mu^2K^2/n$, the signal-to-noise ratio, exceeds $1/e$. This extends a result by Deshpande and Montanari previously obtained for $K=\Theta(\sqrt{n}).$ In addition, the algorithm can be extended to provide exact recovery whenever information-theoretically possible and achieve the information limit of exact recovery as long as $K \geq \frac{n}{\log n} (\frac{1}{8e} + o(1))$. The total running time of the algorithm is $O(n^2\log n)$. Another version of the submatrix localization problem, known as noisy biclustering, aims to recover a $K_1\times K_2$ submatrix of elevated mean $\mu$ in a large $n_1\times n_2$ Gaussian matrix. The optimized message passing algorithm and its analysis are adapted to the bicluster problem assuming $\Omega(\sqrt{n_i}) \leq K_i \leq o(n_i)$ and $K_1\asymp K_2.$ A sharp information-theoretic condition for the weak recovery of both clusters is also identified.
Quantum cohomology of the Springer resolution

Abstract Let G denote a complex, semi-simple, simply-connected group and B its associated flag variety. We identify the equivariant quantum differential equation for the cotangent bundle T ⁎ B with the affine Knizhnik–Zamolodchikov connection of Cherednik and Matsuo. This recovers Kimʼs description of quantum cohomology of B as a limiting case. A parallel result is proven for resolutions of the Slodowy slices. Extension to arbitrary symplectic resolutions is discussed.
Exact Reconstruction From Insertions in Synchronization Codes

This paper studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and nonbinary sequences from synchronization (insertion/deletion-correcting) codes. These sequences have been corrupted by a fixed number of symbol insertions (larger than the minimum edit distance of the code), yielding a number of distinct traces to be used for reconstruction. We wish to know the minimum number of traces needed for exact reconstruction. This is a general version of a problem tackled by Levenshtein for uncoded sequences. We introduce an exact formula for the maximum number of common supersequences shared by sequences at a certain edit distance, yielding an upper bound on the number of distinct traces necessary to guarantee exact reconstruction. Without specific knowledge of the code words, this upper bound is tight. We apply our results to the famous single deletion/insertion-correcting Varshamov–Tenengolts (VT) codes and show that a significant number of VT code word pairs achieve the worst case number of outputs needed for exact reconstruction. We also consider extensions to other channels, such as adversarial deletion and insertion/deletion channels and probabilistic channels.
A Royal Road to Quantum Theory (or Thereabouts).

This paper fails to derive quantum mechanics from a few simple postulates. However, it gets very close, and does so without much exertion. More precisely, I obtain a representation of finite-dimensional probabilistic systems in terms of Euclidean Jordan algebras, in a strikingly easy way, from simple assumptions. This provides a framework within which real, complex and quaternionic QM can play happily together and allows some (but not too much) room for more exotic alternatives. (This is a leisurely summary, based on recent lectures, of material from the papers arXiv:1206:2897 and arXiv:1507.06278, the latter joint work with Howard Barnum and Matthew Graydon. Some further ideas are also explored, developing the connection between conjugate systems and the possibility of forming stable measurement records and making connections between this approach and the categorical approach to quantum theory.)
The No Gap Conjecture for tame hereditary algebras

Abstract The “No Gap Conjecture” of Brustle–Dupont–Perotin states that the set of lengths of maximal green sequences for hereditary algebras over an algebraically closed field has no gaps. This follows from a stronger conjecture that any two maximal green sequences can be “polygonally deformed” into each other. We prove this stronger conjecture for all tame hereditary algebras over any field, equivalently, for any acyclic tame skew-symmetrizable exchange matrix.
Assessing Language Proficiency from Eye Movements in Reading

We present a novel approach for determining learners’ second language proficiency which utilizes behavioral traces of eye movements during reading. Our approach provides stand-alone eyetracking based English proficiency scores which reflect the extent to which the learner’s gaze patterns in reading are similar to those of native English speakers. We show that our scores correlate strongly with standardized English proficiency tests. We also demonstrate that gaze information can be used to accurately predict the outcomes of such tests. Our approach yields the strongest performance when the test taker is presented with a suite of sentences for which we have eyetracking data from other readers. However, it remains effective even using eyetracking with sentences for which eye movement data have not been previously collected. By deriving proficiency as an automatic byproduct of eye movements during ordinary reading, our approach offers a potentially valuable new tool for second language proficiency assessment. More broadly, our results open the door to future methods for inferring reader characteristics from the behavioral traces of reading.
Blow up and regularity for fractal Burgers equation

The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite time blow up for the power of Laplacian α < 1/2, and global existence as well as analyticity of solution for α ≥ 1/2. We also prove the existence of solutions with very rough initial data u0 ∈ Lp, 1 < p < ∞. Many of the results can be extended to a more general class of equations, including the surface quasi-geostrophic equation.
Algebraic multigrid methods

This paper provides an overview of AMG methods for solving large-scale systems of equations, such as those from discretizations of partial differential equations. AMG is often understood as the acronym of ‘algebraic multigrid’, but it can also be understood as ‘abstract multigrid’. Indeed, we demonstrate in this paper how and why an algebraic multigrid method can be better understood at a more abstract level. In the literature, there are many different algebraic multigrid methods that have been developed from different perspectives. In this paper we try to develop a unified framework and theory that can be used to derive and analyse different algebraic multigrid methods in a coherent manner. Given a smoother for a matrix , such as Gauss–Seidel or Jacobi, we prove that the optimal coarse space of dimension is the span of the eigenvectors corresponding to the first eigenvectors (with ). We also prove that this optimal coarse space can be obtained via a constrained trace-minimization problem for a matrix associated with , and demonstrate that coarse spaces of most existing AMG methods can be viewed as approximate solutions of this trace-minimization problem. Furthermore, we provide a general approach to the construction of quasi-optimal coarse spaces, and we prove that under appropriate assumptions the resulting two-level AMG method for the underlying linear system converges uniformly with respect to the size of the problem, the coefficient variation and the anisotropy. Our theory applies to most existing multigrid methods, including the standard geometric multigrid method, classical AMG, energy-minimization AMG, unsmoothed and smoothed aggregation AMG and spectral AMGe.
CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networks.

Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial distortion of neural networks (with ReLU activations) has been shown to be an NP-complete problem, obtaining a non-trivial lower bound of minimum distortion as a provable robustness guarantee is possible. However, most previous works only focused on simple fully-connected layers (multilayer perceptrons) and were limited to ReLU activations. This motivates us to propose a general and efficient framework, CNN-Cert, that is capable of certifying robustness on general convolutional neural networks. Our framework is general – we can handle various architectures including convolutional layers, max-pooling layers, batch normalization layer, residual blocks, as well as general activation functions; our approach is efficient – by exploiting the special structure of convolutional layers, we achieve up to 17 and 11 times of speed-up compared to the state-of-the-art certification algorithms (e.g. Fast-Lin, CROWN) and 366 times of speed-up compared to the dual-LP approach while our algorithm obtains similar or even better verification bounds. In addition, CNN-Cert generalizes state-of-the-art algorithms e.g. Fast-Lin and CROWN. We demonstrate by extensive experiments that our method outperforms state-of-the-art lowerbound-based certification algorithms in terms of both bound quality and speed.
Unimodular rows over monoid rings

Abstract For a commutative Noetherian ring R of dimension d and a commutative cancellative monoid M, the elementary action on unimodular n-rows over the monoid ring R [ M ] is transitive for n ≥ max ⁡ ( d + 2 , 3 ) . The starting point is the case of polynomial rings, considered by A. Suslin in the 1970s. The main result completes a project, initiated in the early 1990s, and suggests a new direction in the study of K-theory of monoid rings.
Scalable Algorithms for Learning High-Dimensional Linear Mixed Models.

Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data. State-of-the-art learning algorithms require computational complexity which depends at least linearly on the dimension $p$ of the covariates, and often use heuristics that do not offer theoretical guarantees. We present scalable algorithms for learning high-dimensional LMMs with sublinear computational complexity dependence on $p$. Key to our approach are novel dual estimators which use only kernel functions of the data, and fast computational techniques based on the subsampled randomized Hadamard transform. We provide theoretical guarantees for our learning algorithms, demonstrating the robustness of parameter estimation. Finally, we complement the theory with experiments on large synthetic and real data.
Dynamic consistency and decision making under vacuous belief

The ideas about decision making under ignorance in economics are combined with the ideas about uncertainty representation in computer science. The combination sheds new light on the question of how artificial agents can act in a dynamically consistent manner. The notion of sequential consistency is formalized by adapting the law of iterated expectation for plausibility measures. The necessary and sufficient condition for a certainty equivalence operator for Nehring-Puppe's preference to be sequentially consistent is given. This result sheds light on the models of decision making under uncertainty.