nils-herrmann/clean_scirepeval huggingface dataset:
Precisely Verifying the Null Space Conditions in Compressed Sensing: A Sandwiching Algorithm

In this paper, we propose new efficient algorithms to verify the null space condition in compressed sensing (CS). Given an $(n-m) \times n$ ($m>0$) CS matrix $A$ and a positive $k$, we are interested in computing $\displaystyle \alpha_k = \max_{\{z: Az=0,z\neq 0\}}\max_{\{K: |K|\leq k\}}$ ${\|z_K \|_{1}}{\|z\|_{1}}$, where $K$ represents subsets of $\{1,2,...,n\}$, and $|K|$ is the cardinality of $K$. In particular, we are interested in finding the maximum $k$ such that $\alpha_k < {1}{2}$. However, computing $\alpha_k$ is known to be extremely challenging. In this paper, we first propose a series of new polynomial-time algorithms to compute upper bounds on $\alpha_k$. Based on these new polynomial-time algorithms, we further design a new sandwiching algorithm, to compute the \emph{exact} $\alpha_k$ with greatly reduced complexity. When needed, this new sandwiching algorithm also achieves a smooth tradeoff between computational complexity and result accuracy. Empirical results show the performance improvements of our algorithm over existing known methods; and our algorithm outputs precise values of $\alpha_k$, with much lower complexity than exhaustive search.
Preserving differential privacy under finite-precision semantics

The approximation introduced by finite-precision representation of continuous data can induce arbitrarily large information leaks even when the computation using exact semantics is secure. Such leakage can thus undermine design efforts aimed at protecting sensitive information. We focus here on differential privacy, an approach to privacy that emerged from the area of statistical databases and is now widely applied also in other domains. In this approach, privacy is protected by adding noise to the values correlated to the private data. The typical mechanisms used to achieve differential privacy have been proved correct in the ideal case in which computations are made using infinite-precision semantics. In this paper, we analyze the situation at the implementation level, where the semantics is necessarily limited by finite precision, i.e., the representation of real numbers and the operations on them are rounded according to some level of precision. We show that in general there are violations of the differential privacy property, and we study the conditions under which we can still guarantee a limited (but, arguably, acceptable) variant of the property, under only a minor degradation of the privacy level.
Mean-Variance and Expected Utility: The Borch Paradox

The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-variance (MV) introduced in the 1950s by Markowitz. Under the MV framework, each available investment opportunity ("asset") or portfolio is represented in just two dimensions by the ex ante mean and standard deviation $(\mu,\sigma)$ of the financial return anticipated from that investment. Utility adherents consider that in general MV methods are logically incoherent. Most famously, Norwegian insurance theorist Borch presented a proof suggesting that two-dimensional MV indifference curves cannot represent the preferences of a rational investor (he claimed that MV indifference curves "do not exist"). This is known as Borch's paradox and gave rise to an important but generally little-known philosophical literature relating MV to EU. We examine the main early contributions to this literature, focussing on Borch's logic and the arguments by which it has been set aside.
ROBUST PORTFOLIOS AND WEAK INCENTIVES IN LONG‐RUN INVESTMENTS

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage‐free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not always convex.
Information thermodynamics on causal networks.

We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel generalizations of the second law of thermodynamics and the fluctuation theorem, which include an informational quantity characterized by the topology of the causal network. Our result implies that the entropy production in a single system in the presence of multiple other systems is bounded by the information flow between these systems. We demonstrate our general result by a simple model of biochemical adaptation.
Resolving Structural Variability in Network Models and the Brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known in general about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar graph metrics, but presented here in a more complete statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus specifically on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling—in addition to several summary statistics, including the mean clustering coefficient, the shortest path-length, and the network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be physically embedded in anatomical brain regions tend to produce distributions that are most similar to the corresponding measurements for the brain. We also find that network models hardcoded to display one network property (e.g., assortativity) do not in general simultaneously display a second (e.g., hierarchy). This relative independence of network properties suggests that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.
Assessing Student Learning in Middle-Division Classical Mechanics/Math Methods

Reliable and validated assessments of introductory physics have been instrumental in driving curricular and pedagogical reforms that lead to improved student learning. As part of an effort to systematically improve our sophomore-level Classical Mechanics and Math Methods course (CM 1) at CU Boulder, we are developing a tool to assess student learning of CM 1 concepts in the upper-division. The Colorado Classical Mechanics/Math Methods Instrument (CCMI) builds on faculty-consensus learning goals and systematic observations of student difficulties. The result is a 9-question open-ended post-test that probes student learning in the first half of a two-semester classical mechanics / math methods sequence. In this paper, we describe the design and development of this instrument, its validation, and measurements made in classes at CU Boulder.
Dynamical Dark Matter and the positron excess in light of AMS results

The AMS-02 experiment has recently released data which confirms a rise in the cosmic-ray positron fraction as a function of energy up to approximately 350 GeV. Over the past decade, attempts to interpret this positron excess in terms of dark-matter decays have become increasingly complex and have led to a number of general expectations about the decaying dark-matter particles: such particles cannot undergo simple two-body decays to leptons, for example, and they must have rather heavy TeV-scale masses. In this paper, by contrast, we show that Dynamical Dark Matter (DDM) can not only match existing AMS-02 data on the positron excess, but also accomplish this feat with significantly lighter dark-matter constituents undergoing simple two-body decays to leptons. Moreover, we demonstrate that this can be done without running afoul of numerous other competing constraints from FERMI and Planck on decaying dark matter. Finally, we demonstrate that the Dynamical Dark Matter framework makes a fairly robust prediction that the positron fraction should level off and then remain roughly constant out to approximately 1 TeV, without experiencing any sharp downturns. Indeed, if we interpret the positron excess in terms of decaying dark matter, we find that the existence of a plateau in the positron fraction at energies less than 1 TeV may be taken as a "smoking gun" of Dynamical Dark Matter.
Kaluza–Klein-type models of de Sitter and Poincaré gauge theories of gravity

We construct Kaluza–Klein-type models with a de Sitter or Minkowski bundle in the de Sitter or Poincaré gauge theory of gravity, respectively. A manifestly gauge-invariant formalism has been given. The gravitational dynamics is constructed by the geometry of the de Sitter or Minkowski bundle and a global section which plays an important role in the gauge-invariant formalism. Unlike the old Kaluza–Klein-type models of gauge theory of gravity, a suitable cosmological term can be obtained in the Lagrangian of our models and the models in the spin-current-free and torsion-free limit will come back to general relativity with a corresponding cosmological term. We also generalize the results to the case with a variable cosmological term.
Some Remarks on the Logic of Quantum Gravity

We discuss some conceptual issues that any approach to quantum gravity has to confront. In particular, it is argued that one has to find a theory that can be interpreted in a realist manner, because theories with an instrumentalist interpretation are problematic for several wellknown reasons. Since the Hilbert space formalism almost inevitably forces an instrumentalist interpretation on us, we suggest that a theory of quantum gravity should not be based on the Hilbert space formalism. We briefly sketch the topos approach, which makes use of the internal logic of a topos associated with a quantum system and comes with a natural (neo-)realist interpretation. Finally, we make some remarks on the relation between system logic and metalogic.
Quantum instability of the emergent universe

We perform a semi-classical analysis of the Emergent Universe scenario for inflation. Fixing the background, and taking the inflaton to be homogenous, we cast the inflaton’s evolution as a onedimensional quantum mechanics problem. The potential is taken to be flat or linear, as an approximation to the monotonic and slowly-varying asymptotic behavior of the Emergent Universe potential. We find that the tuning required over a long time scale for this inflationary scenario is unstable quantum mechanically. Considering the inflaton field value as a wavepacket, the spreading of the wavepacket destroys any chance of both starting and ending with a well-formed state. Thus, one cannot have an Einstein static universe to begin with that evolves into a well-defined beginning to inflation a long time later.
Higgs seesaw mechanism as a source for dark energy.

Motivated by the seesaw mechanism for neutrinos which naturally generates small neutrino masses, we explore how a small grand-unified-theory-scale mixing between the standard model Higgs boson and an otherwise massless hidden sector scalar can naturally generate a small mass and vacuum expectation value for the new scalar which produces a false vacuum energy density contribution comparable to that of the observed dark energy dominating the current expansion of the Universe. This provides a simple and natural mechanism for producing the correct scale for dark energy, even if it does not address the long-standing question of why much larger dark energy contributions are not produced from the visible sector. The new scalar produces no discernible signatures in existing terrestrial experiments so that one may have to rely on other cosmological tests of this idea.
Scientific reach of multiton-scale dark matter direct detection experiments

The next generation of large scale WIMP direct detection experiments have the potential to go beyond the discovery phase and reveal detailed information about both the particle physics and astrophysics of dark matter. We report here on early results arising from the development of a detailed numerical code modeling the proposed DARWIN detector, involving both liquid argon and xenon targets. We incorporate realistic detector physics, particle physics and astrophysical uncertainties and demonstrate to what extent two targets with similar sensitivities can remove various degeneracies and allow a determination of dark matter cross sections and masses while also probing rough aspects of the dark matter phase space distribution. We find that, even assuming dominance of spin-independent scattering, multi-ton scale experiments still have degeneracies that depend sensitively on the dark matter mass, and on the possibility of isospin violation and inelasticity in interactions. We find that these experiments are best able to discriminate dark matter properties for dark matter masses less than around 200 GeV. In addition, and somewhat surprisingly, the use of two targets gives only a small improvement (aside from the advantage of different systematics associated with any claimed signal) in the ability to pin down dark matter parameters when compared with one target of larger exposure.
arXiv E‐prints and the journal of record: An analysis of roles and relationships

Since its creation in 1991, arXiv has become central to the diffusion of research in a number of fields. Combining data from the entirety of arXiv and the Web of Science (WoS), this article investigates (a) the proportion of papers across all disciplines that are on arXiv and the proportion of arXiv papers that are in the WoS, (b) the elapsed time between arXiv submission and journal publication, and (c) the aging characteristics and scientific impact of arXiv e‐prints and their published version. It shows that the proportion of WoS papers found on arXiv varies across the specialties of physics and mathematics, and that only a few specialties make extensive use of the repository. Elapsed time between arXiv submission and journal publication has shortened but remains longer in mathematics than in physics. In physics, mathematics, as well as in astronomy and astrophysics, arXiv versions are cited more promptly and decay faster than WoS papers. The arXiv versions of papers—both published and unpublished—have lower citation rates than published papers, although there is almost no difference in the impact of the arXiv versions of published and unpublished papers.
Quark propagation in the instantons of lattice QCD

We quantitatively examine the extent to which instanton degress of freedom, contained within standard Monte-carlo generated gauge-field configurations, can maintain the characteristic features of the mass and renormalisation functions of the non-perturbative quark propagator. We use over-improved stout-link smearing to isolate instanton effects on the lattice. Using a variety of measures, we illustrate how gauge fields consisting almost solely of instanton-like objects are produced after only 50 sweeps of smearing. We find a full vacuum, with a packing fraction more than three times larger than phenomenological models predict. We calculate the overlap quark propagator on these smeared configurations, and find that even at high levels of smearing the majority of the characteristic features of the propagator are reproduced. We thus conclude that instantons contained within standard Monte-carlo generated gauge-field configurations are the degrees of freedom responsible for the dynamical generation of mass observed in lattice QCD.
Quantifying Long-Term Scientific Impact

Citation Grabbers Is there quantifiable regularity and predictability in citation patterns? It is clear that papers that have been cited frequently tend to accumulate more citations. It is also clear that, with time, even the most novel paper loses its currency. Some papers, however, seem to have an inherent “fitness” that can be interpreted as a community's response to the research. Wang et al. (p. 127; see the Perspective by Evans) developed a mechanistic model to predict citation history. The model links a paper's ultimate impact, represented by the total number of citations the paper will ever receive, to a single measurable parameter inferred from its early citation history. The model was used to identify factors that influence a journal's impact factor. Early citation history can be used to model the total number of citations a paper will receive and to compare journals.  Is there long-term predictability in citation patterns? Here, we derive a mechanistic model for the citation dynamics of individual papers, allowing us to collapse the citation histories of papers from different journals and disciplines into a single curve, indicating that all papers tend to follow the same universal temporal pattern. The observed patterns not only help us uncover basic mechanisms that govern scientific impact but also offer reliable measures of influence that may have potential policy implications.
Rethinking Abstractions for Big Data: Why, Where, How, and What

Big data refers to large and complex data sets that, under existing approaches, exceed the capacity and capability of current compute platforms, systems software, analytical tools and human understanding. Numerous lessons on the scalability of big data can already be found in asymptotic analysis of algorithms and from the high-performance computing (HPC) and applications communities. However, scale is only one aspect of current big data trends; fundamentally, current and emerging problems in big data are a result of unprecedented complexity--in the structure of the data and how to analyze it, in dealing with unreliability and redundancy, in addressing the human factors of comprehending complex data sets, in formulating meaningful analyses, and in managing the dense, power-hungry data centers that house big data. 
The computer science solution to complexity is finding the right abstractions, those that hide as much triviality as possible while revealing the essence of the problem that is being addressed. The "big data challenge" has disrupted computer science by stressing to the very limits the familiar abstractions which define the relevant subfields in data analysis, data management and the underlying parallel systems. As a result, not enough of these challenges are revealed by isolating abstractions in a traditional software stack or standard algorithmic and analytical techniques, and attempts to address complexity either oversimplify or require low-level management of details. The authors believe that the abstractions for big data need to be rethought, and this reorganization needs to evolve and be sustained through continued cross-disciplinary collaboration.
Sparse Auto-Regressive: Robust Estimation of AR Parameters

In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation difficult, so it should be robust against them. Moreover for coding purposes I will show that it is desired the residual of auto-regression be sparse. To these aims, I first assume a multivariate Gaussian prior on the residual and then obtain the estimation. Two simple simulations have been done on spectrum estimation and speech coding.
Sparse Recovery of Streaming Signals Using $\ell_1$-Homotopy

Most of the existing sparse-recovery methods assume a static system: the signal is a finite-length vector for which a fixed set of measurements and sparse representation are available and an l1 problem is solved for the reconstruction. However, the same representation and reconstruction framework is not readily applicable in a streaming system: the signal changes over time, and it is measured and reconstructed sequentially over small intervals. This is particularly desired when dividing signals into disjoint blocks and processing each block separately is infeasible or inefficient. In this paper, we discuss two streaming systems and a new homotopy algorithm for quickly solving the associated l1 problems: 1) recovery of smooth, time-varying signals for which, instead of using block transforms, we use lapped orthogonal transforms for sparse representation and 2) recovery of sparse, time-varying signals that follows a linear dynamic model. For both systems, we iteratively process measurements over a sliding interval and solve a weighted l1-norm minimization problem for estimating sparse coefficients. Since we estimate overlapping portions of the signal while adding and removing measurements, instead of solving a new l1 program as the system changes, we use available signal estimates as starting point in a homotopy formulation and update the solution in a few simple steps. We demonstrate with numerical experiments that our proposed streaming recovery framework provides better reconstruction compared to the methods that represent and reconstruct signals as independent, disjoint blocks, and that our proposed homotopy algorithm updates the solution faster than the current state-of-the-art solvers.
Making mean-variance hedging implementable in a partially observable market

The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literature treats the MVH problem by the duality method, here we study an equivalent system consisting of three BSDEs and try to provide more explicit expressions directly implementable by practitioners. Under the Bayesian and Kalman–Bucy frameworks, we find that a relevant BSDE can yield a semi-closed solution via a simple set of ODEs which allow quick numerical evaluation. This renders the remaining problems equivalent to solving European contingent claims under a new forward measure, and it is straightforward to obtain a forward looking non-sequential Monte Carlo simulation scheme. We also give a special example where the hedging position is available in a semi-closed form. For more generic set-ups, we provide explicit expressions of an approximate hedging portfolio by an asymptotic expansion. These analytic expressions not only allow the hedgers to update the hedging positions in real time but also make a direct analysis of the terminal distribution of the hedged portfolio feasible by standard Monte Carlo simulation.