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We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message passing algorithm, on the random $k$-XORSAT problem. Specifically, we derive an explicit threshold up to which the algorithm succeeds with a strictly positive probability $\Omega(1)$ that we compute explicitly, but beyond which the algorithm with high probability fails to find a satisfying assignment. In addition, we analyse a thought experiment called the decimation process for which we identify a (non-) reconstruction and a condensation phase transition. The main results of the present work confirm physics predictions from [RTS: J. Stat. Mech. 2009] that link the phase transitions of the decimation process with the performance of the algorithm, and improve over partial results from a recent article [Yung: Proc. ICALP 2024].

One can recover vectors from $\mathbb{R}^m$ with arbitrary precision, using only $\lceil \log_2(m+1)\rceil +1$ continuous measurements that are chosen adaptively. This surprising result is explained and discussed, and we present applications to infinite-dimensional approximation problems., Comment: 12 pages

Who ends up in the teacher workforce is greatly influenced by who is admitted into teacher education programs (TEPs). To better understand how the preferences of teacher education faculty might shape admissions of STEM teacher candidates, we surveyed faculty who teach content or methods courses to STEM teacher candidates across five universities. Faculty reported that they most value information collected from individual interviews with applicants and data on the number of STEM courses taken in college and their performance in these courses, and least value data on university admissions tests, high school GPA, and teacher licensure test scores. When we investigate faculty members' revealed preferences through a conjoint analysis, we find that faculty most value applicants who have worked with students from diverse backgrounds and applicants from a marginalized racial or ethnic community, and least value whether they received high grades in math and/or science courses. Finally, we find significant variation in these perceptions across respondents in different faculty roles, who teach different courses, and from different institutions: for example, Arts and Sciences faculty tend to value TEP applicants' performance in college STEM courses relatively more than STEM education faculty, while STEM education faculty tend to value applicants' race and ethnicity relatively more than Arts and Sciences faculty.

This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not over-conservative. This combination results in a bilevel optimization problem. For solving this problem, a three-stage algorithm which uses adaptive discretization of the uncertainty set via two criteria is presented and its convergence is proven. The algorithm is applicable for an example of optimizing a robust pump operation plan for a drinking water supply system facing uncertain demand. The algorithm shows a notable ability to scale, presenting an opportunity to solve larger instances that might challenge existing optimization approaches., Comment: 25 pages, 3 figures

We present a simple universal algorithm for high-dimensional integration which has the optimal error rate (independent of the dimension) in all weighted Korobov classes both in the randomized and the deterministic setting. Our theoretical findings are complemented by numerical tests., Comment: 18 pages. MATLAB code for numerical tests is attached

In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other items. In the (over-)idealized noiseless setting, tests are positive exactly if any of the tested items are defective. We study a more realistic model in which observed test results are subject to noise, i.e., tests can display false positive or false negative results with constant positive probabilities. We determine precise constants $c$ such that $cn\log n$ tests are required to recover the infection status of every individual for both adaptive and non-adaptive group testing: in the former, the selection of groups to test can depend on previously observed test results, whereas it cannot in the latter. Additionally, for both settings, we provide efficient algorithms that identify all defective items with the optimal amount of tests with high probability. Thus, we completely solve the problem of binary noisy group testing in the studied setting.

To alleviate the suboptimal performance of belief propagation (BP) decoding of short low-density parity-check (LDPC) codes, a plethora of improved decoding algorithms has been proposed over the last two decades. Many of these methods can be described using the same general framework, which we call ensemble decoding: A set of independent constituent decoders works in parallel on the received sequence, each proposing a codeword candidate. From this list, the maximum likelihood (ML) decision is designated as the decoder output. In this paper, we qualitatively and quantitatively compare different realizations of the ensemble decoder, namely multiple-bases belief propagation (MBBP), automorphism ensemble decoding (AED), scheduling ensemble decoding (SED), noise-aided ensemble decoding (NED) and saturated belief propagation (SBP). While all algorithms can provide gains over traditional BP decoding, ensemble methods that exploit the code structure, such as MBBP and AED, typically show greater performance improvements., Comment: 6 pages, 7 figures, submitted to IEEE for possible publication

In this paper, we propose a data-driven algorithm to design rate- and length-flexible polar codes. While the algorithm is very general, a particularly appealing use case is the design of codes for automorphism ensemble decoding (AED), a promising decoding algorithm for ultra-reliable low-latency communications (URLLC) and massive machine-type communications (mMTC) applications. To this end, theoretic results on nesting of symmetric polar codes are derived, which give hope in finding a fully nested, rate-compatible sequence suitable for AED. Using the proposed algorithms, such a flexible polar code design for automorphism ensemble successive cancellation (SC) decoding is constructed, outperforming existing code designs for AED and also the 5G polar code under cyclic redundancy check (CRC)-aided successive cancellation list (SCL) decoding., Comment: 6 pages, 2 figures, submitted to IEEE for possible publication

We present Connected-Component~(CC)-Metrics, a novel semantic segmentation evaluation protocol, targeted to align existing semantic segmentation metrics to a multi-instance detection scenario in which each connected component matters. We motivate this setup in the common medical scenario of semantic metastases segmentation in a full-body PET/CT. We show how existing semantic segmentation metrics suffer from a bias towards larger connected components contradicting the clinical assessment of scans in which tumor size and clinical relevance are uncorrelated. To rebalance existing segmentation metrics, we propose to evaluate them on a per-component basis thus giving each tumor the same weight irrespective of its size. To match predictions to ground-truth segments, we employ a proximity-based matching criterion, evaluating common metrics locally at the component of interest. Using this approach, we break free of biases introduced by large metastasis for overlap-based metrics such as Dice or Surface Dice. CC-Metrics also improves distance-based metrics such as Hausdorff Distances which are uninformative for small changes that do not influence the maximum or 95th percentile, and avoids pitfalls introduced by directly combining counting-based metrics with overlap-based metrics as it is done in Panoptic Quality.

In this work, we confront the bound on an ultraviolet cutoff (UV) of a quantum field theory (QFT) proposed by Cohen, Kaplan, and Nelson (CKN) with the latest results of the Dark Energy Spectroscopic Instrument (DESI). The former relates the UV cutoff with an infrared (IR) cutoff of the theory by excluding all states describing a black hole. Identifying now the IR cutoff with the Hubble horizon yields a time-varying contribution of the vacuum energy to the dark energy density of the universe. At the same time the DESI results in combination with other cosmological data point towards a preference of time-varying dark energy models over $\Lambda$CDM., Comment: Prepared for the proceedings of PASCOS 2024 in Vietnam, 5 pages, 2 figures, 1 table; matches version appearing in the proceedings

We assess the potential of neutrino telescopes to discover quantum-gravity-induced decoherence effects modeled in the open-quantum system framework and with arbitrary numbers of active and dark fermion generations, such as particle dark matter or sterile neutrinos. The expected damping of neutrino flavor oscillation probabilities as a function of energy and propagation length thus encodes information about quantum gravity effects and the fermion generation multiplicity in the dark sector. We employ a public Monte-Carlo dataset provided by the IceCube Collaboration to model the detector response and estimate the sensitivity of IceCube to oscillation effects in atmospheric neutrinos induced by the presented model. Our findings confirm the potential of very-large-volume neutrino telescopes to test this class of models and indicate higher sensitivities for increasing numbers of dark fermions., Comment: 18 pages, 8 figures, included systematic effects relevant for the IceCube Neutrino observatory, updated the resulting bounds on the QG parameter, published in JCAP

We study the disassortative stochastic block model with three communities, a well-studied model of graph partitioning and Bayesian inference for which detailed predictions based on the cavity method exist [Decelle et al. (2011)]. We provide strong evidence that for a part of the phase where efficient algorithms exist that approximately reconstruct the communities, inference based on maximum a posteriori (MAP) fails. In other words, we show that there exist modes of the posterior distribution that have a vanishing agreement with the ground truth. The proof is based on the analysis of a graph colouring algorithm from [Achlioptas and Moore (2003)].

Gravity constrains the range of validity of quantum field theory. As has been pointed out by Cohen, Kaplan, and Nelson (CKN), such effects lead to interdependent ultraviolet (UV) and infrared (IR) cutoffs that may stabilize the dark energy of the universe against quantum corrections, if the IR cutoff is set by the Hubble horizon. As a consequence of the cosmic expansion, this argument implies a time-dependent dark energy density. In this paper we confront this idea with recent data from DESI BAO, Hubble and supernova measurements. We find that the CKN model provides a better fit to the data than the $\Lambda$CDM model and can compete with other models of time-dependent dark energy that have been studied so far., Comment: 16 pages, 5 figures, 6 tables; accepted for publication in JCAP

We present bounds between different widths of convex subsets of Banach spaces, including Gelfand and Bernstein widths. Using this, and some relations between widths and minimal errors, we obtain bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. Our results also apply to the approximation of embeddings into the space of bounded functions based on function evaluations, i.e., to sampling recovery in the uniform norm. We conclude with a list of open problems.

We present a Hamiltonian Monte Carlo study of doped perylene $\mathrm{C}_{20}\mathrm{H}_{12}$ described with the Hubbard model. Doped perylene can be used for organic light-emitting diodes (OLEDs) or as acceptor material in organic solar cells. Therefore, central to this study is a scan over charge chemical potential. A variational basis of operators allows for the extraction of the single-particle spectrum through a mostly automatic fitting procedure. Finite chemical potential simulations suffer from a sign problem which we ameliorate through contour deformation. The on-site interaction is kept at $U/\kappa = 2$. Discretization effects are handled through a continuum limit extrapolation. Our first-principles calculation shows significant deviation from non-interacting results especially at large chemical potentials.

We show that the high-temperature expansion of the free energy and arbitrary imaginary-time-ordered connected correlation functions of quantum spin systems can be recursively obtained from the exact renormalization group flow equation for the generating functional of connected spin correlation functions derived by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)]. Our recursive algorithm can be explicitly written down in closed form including all combinatorial factors. We use our method to estimate critical temperatures of Heisenberg magnets from low-order truncations of the inverse spin susceptibility in the static limit. We also calculate the connected correlation function involving three different spin components (chiral non-linear susceptibility) of quantum Heisenberg magnets up to second order in the exchange couplings., Comment: 21 pages, 10 figures

Quark orbital angular momentum in the proton is evaluated via a Lattice QCD calculation of the second Mellin moment of the twist-3 generalized parton distribution $\widetilde{E}_{2T} $ in the forward limit. The connection between this approach to quark orbital angular momentum and approaches previously utilized in Lattice QCD calculations, via generalized transverse momentum-dependent parton distributions and via Ji's sum rule, is reviewed. This connection can be given in terms of Lorentz invariance and equation of motion relations. The calculation of the second Mellin moment of $\widetilde{E}_{2T} $ proceeds via a finite-momentum proton matrix element of a quark bilocal operator with a straight-line gauge connection and separation in both the longitudinal and transverse directions. The dependence on the former component serves to extract the second Mellin moment, whereas the dependence on the latter component provides a transverse momentum cutoff for the matrix element. Furthermore, a derivative of the matrix element with respect to momentum transfer in the forward limit is required, which is obtained using a direct derivative method. The calculation utilizes a clover fermion ensemble at pion mass 317 MeV. The resulting quark orbital angular momentum is consistent with previous evaluations through alternative approaches, albeit with greater statistical uncertainty using a comparable number of samples., Comment: 10 pages, 3 figures, to appear in the proceedings of the 25th International Spin Physics Symposium (SPIN 2023), PoS SPIN2023 (2024) 075

Nationally, more than 75% of individuals who are credentialed to teach are prepared in traditional college- or university-based teacher education programs (TEPs). But the college and employment pathways that prospective teachers take to TEP enrollment and completion have not been comprehensively examined. A better understanding of how credentialed individuals find their way into TEPs helps us understand the sources of new teacher supply early in the prospective teacher pipeline. With that in mind, we analyze pathways into and through TEPs using historical postsecondary and unemployment insurance data from Washington state. We find that the pathways are quite varied with around 40% of bachelor's-level TEP completers spending at least some time in community colleges and less than 40% enrolling and finishing at the same university directly after high school. Pathways to master's TEP completion are even more varied, with almost half of the completers having prior employment experience. For researchers, this varied landscape raises important questions about the relationship between pathways, candidate persistence, and eventual job performance. For policymakers, the results suggest that efforts to recruit the next generation of teachers need to look beyond the pool of students already enrolled at a 4-year university to include students at 2-year colleges or in the labor force who might be interested in entering a TEP.

Gravitational waves (GWs) can alter the neutrino propagation distance and thus affect neutrino oscillations. This can result in a complete disappearance of the oscillatory behavior that competes with other sources of neutrino decoherence. We develop a set of criteria that determines under which conditions neutrino oscillations are sensitive to this effect. We find that current or near future neutrino oscillation experiments are not sufficiently sensitive to coherent GW signals but may probe the stochastic gravitational wave background if the energy resolution improves drastically by several orders of magnitude., Comment: 28 pages, 5 figures, 2 tables; fixed numerical mistake

Prior research has connected characteristics of cooperating teachers who supervise student teaching to performance measures of the teacher candidates they host, suggesting more effective teachers may also be better mentors. The specific measures of cooperating teacher effectiveness considered in this prior literature (value added and performance evaluations), however, are infrequently observable to individuals responsible for student teaching placements. In this paper, we consider a more easily observed proxy for mentor effectiveness: National Board (NB) Certification. We find that NB teachers are considerably more likely to host candidates than other teachers, candidates supervised by NB teachers are slightly more likely to be hired within three years, and these candidates have slightly lower value added in English language arts than their peers, all else being equal. We find no significant relationship between cooperating teacher NB certification and candidates' later attrition and value added in math. We conclude that individuals and policies seeking to leverage student teaching placements to improve student and teacher outcomes may need to focus on less easily observable proxies of cooperating teacher quality than NB certification status.

We study the problem of identifying a small set $k\sim n^\theta$, $0<\theta<1$, of infected individuals within a large population of size $n$ by testing groups of individuals simultaneously. All tests are conducted concurrently. The goal is to minimise the total number of tests required. In this paper we make the (realistic) assumption that tests are noisy, i.e.\ that a group that contains an infected individual may return a negative test result or one that does not contain an infected individual may return a positive test results with a certain probability. The noise need not be symmetric. We develop an algorithm called SPARC that correctly identifies the set of infected individuals up to $o(k)$ errors with high probability with the asymptotically minimum number of tests. Additionally, we develop an algorithm called SPEX that exactly identifies the set of infected individuals w.h.p. with a number of tests that matches the information-theoretic lower bound for the constant column design, a powerful and well-studied test design.

We show that there are sampling projections on arbitrary $n$-dimensional subspaces of $B(D)$ with at most $2n$ samples and norm of order $\sqrt{n}$, where $B(D)$ is the space of complex-valued bounded functions on a set $D$. This gives a more explicit form of the Kadets-Snobar theorem for the uniform norm and improves upon Auerbach's lemma. We discuss consequences for optimal recovery in $L_p$.

The widespread application of machine learning techniques to biomedical data has produced many new insights into disease progression and improving clinical care. Inspired by the flexibility and interpretability of graphs (networks), as well as the potency of sequence models like transformers and higher-order networks (HONs), we propose a method that identifies combinations of risk factors for a given outcome and accurately encodes these higher-order relationships in a graph. Using historical data from 913,475 type 2 diabetes (T2D) patients, we found that, compared to other approaches, the proposed networks encode significantly more information about the progression of T2D toward a variety of outcomes. We additionally demonstrate how structural information from the proposed graph can be used to augment the performance of transformer-based models on predictive tasks, especially when the data are noisy. By increasing the order, or memory, of the graph, we show how the proposed method illuminates key risk factors while successfully ignoring noisy elements, which facilitates analysis that is simultaneously accurate and interpretable.

The second Mellin moments $\langle x\rangle$ of the nucleon's unpolarized, polarized, and transversity parton distribution functions (PDFs) are computed. Two lattice QCD ensembles at the physical pion mass are used: these were generated using a tree-level Symanzik-improved gauge action and 2+1 flavour tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. The moments are extracted from forward matrix elements of local leading twist operators. We determine renomalization factors in RI-(S)MOM and match to $\overline{\mathrm{MS}}$ at scale $2\,\mathrm{GeV}$. Our findings show that operators that exhibit vanishing kinematics at zero momentum can have significantly reduced excited-state contamination. The resulting polarized moment is used to quantify the longitudinal contribution to the quark spin-orbit correlation. All our results agree within two sigma with previous lattice results.