@inproceedings{18230, abstract = {A variety of complex systems, including social and communication networks, financial markets, biology, and neuroscience are modeled using temporal graphs that contain a set of nodes and directed timestamped edges. Temporal motifs in temporal graphs are generalized from subgraph patterns in static graphs in that they also account for edge ordering and time duration, in addition to the graph structure. Mining temporal motifs is a fundamental problem used in several application domains. However, existing software frameworks offer suboptimal performance due to high algorithmic complexity and irregular memory accesses of temporal motif mining.This paper presents Mint—a novel accelerator architecture and a programming model for mining temporal motifs efficiently. We first divide this workload into three fundamental tasks: search, book-keeping, and backtracking. Based on this, we propose a task-centric programming model that enables decoupled, asynchronous execution. This model unlocks massive opportunities for parallelism, and allows storing task context information on-chip. To best utilize the proposed programming model, we design a domain-specific hardware accelerator using its data path and memory subsystem design to cater to the unique workload characteristics of temporal motif mining. To further improve performance, we propose a novel optimization called search index memoization that significantly reduces memory traffic. We comprehensively compare the performance of Mint with state-of-the-art temporal motif mining software frameworks (both approximate and exact) running on both CPU and GPU, and show 9×−2576× benefit in performance.}, author = {Talati, Nishil and Ye, Haojie and Vedula, Sanketh and Chen, Kuan-Yu and Chen, Yuhan and Liu, Daniel and Yuan, Yichao and Blaauw, David and Bronstein, Alexander and Mudge, Trevor and Dreslinski, Ronald}, booktitle = {55th IEEE/ACM International Symposium on Microarchitecture}, location = {Chicago, IL, United States}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Mint: An accelerator for mining temporal motifs}}, doi = {10.1109/micro56248.2022.00089}, year = {2022}, } @inproceedings{18231, abstract = {The success of learning with noisy labels (LNL) methods relies heavily on the success of a warm-up stage where standard supervised training is performed using the full (noisy) training set. In this paper, we identify a "warm-up obstacle": the inability of standard warm-up stages to train high quality feature extractors and avert memorization of noisy labels. We propose "Contrast to Divide" (C2D), a simple framework that solves this problem by pre-training the feature extractor in a self-supervised fashion. Using self-supervised pre-training boosts the performance of existing LNL approaches by drastically reducing the warm-up stage's susceptibility to noise level, shortening its duration, and improving extracted feature quality. C2D works out of the box with existing methods and demonstrates markedly improved performance, especially in the high noise regime, where we get a boost of more than 27% for CIFAR-100 with 90% noise over the previous state of the art. In real-life noise settings, C2D trained on mini-WebVision outperforms previous works both in WebVision and ImageNet validation sets by 3% top-1 accuracy. We perform an in-depth analysis of the framework, including investigating the performance of different pre-training approaches and estimating the effective upper bound of the LNL performance with semi-supervised learning. Code for reproducing our experiments is available at https://github.com/ContrastToDivide/C2D.}, author = {Zheltonozhskii, Evgenii and Baskin, Chaim and Mendelson, Avi and Bronstein, Alexander and Litany, Or}, booktitle = {IEEE/CVF Winter Conference on Applications of Computer Vision}, location = {Waikoloa, HI, United States}, pages = {387--397}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Contrast to divide: Self-supervised pre-training for learning with noisy labels}}, doi = {10.1109/wacv51458.2022.00046}, year = {2022}, } @article{18232, abstract = {Cross-modal retrieval aims to retrieve related items across different modalities, for example, using an image query to retrieve related text. The existing deep methods ignore both the intra-modal and inter-modal intra-class low-rank structures when fusing various modalities, which decreases the retrieval performance. In this paper, two deep models (denoted as ILCMR and Semi-ILCMR) based on intra-class low-rank regularization are proposed for supervised and semi-supervised cross-modal retrieval, respectively. Specifically, ILCMR integrates the image network and text network into a unified framework to learn a common feature space by imposing three regularization terms to fuse the cross-modal data. First, to align them in the label space, we utilize semantic consistency regularization to convert the data representations to probability distributions over the classes. Second, we introduce an intra-modal low-rank regularization, which encourages the intra-class samples that originate from the same space to be more relevant in the common feature space. Third, an inter-modal low-rank regularization is applied to reduce the cross-modal discrepancy. To enable the low-rank regularization to be optimized using automatic gradients during network back-propagation, we propose the rank-r approximation and specify the explicit gradients for theoretical completeness. In addition to the three regularization terms that rely on label information incorporated by ILCMR, we propose Semi-ILCMR in the semi-supervised regime, which introduces a low-rank constraint before projecting the general representations into the common feature space. Extensive experiments on four public cross-modal datasets demonstrate the superiority of ILCMR and Semi-ILCMR over other state-of-the-art methods.}, author = {Kang, Peipei and Lin, Zehang and Yang, Zhenguo and Fang, Xiaozhao and Bronstein, Alexander and Li, Qing and Liu, Wenyin}, issn = {1573-7497}, journal = {Applied Intelligence}, pages = {33--54}, publisher = {Springer Nature}, title = {{Intra-class low-rank regularization for supervised and semi-supervised cross-modal retrieval}}, doi = {10.1007/s10489-021-02308-3}, volume = {52}, year = {2022}, } @misc{18291, author = {Katsaros, Georgios and Jirovec, Daniel}, publisher = {Institute of Science and Technology Austria}, title = {{Dynamics of Hole Singlet-Triplet Qubits with Large 𝑔-Factor Differences}}, doi = {10.15479/AT:ISTA:18291}, year = {2022}, } @unpublished{18293, abstract = {Given a non-singular diagonal cubic hypersurface X⊂Pn−1 over Fq(t) with char(Fq)≠3, we show that the number of rational points of height at most |P| is O(|P|3+ε) for n=6 and O(|P|2+ε) for n=4. In fact, if n=4 and char(Fq)>3 we prove that the number of rational points away from any rational line contained in X is bounded by O(|P|3/2+ε). From the result in 6 variables we deduce weak approximation for diagonal cubic hypersurfaces for n≥7 over Fq(t) when char(Fq)>3 and handle Waring's problem for cubes in 7 variables over Fq(t) when char(Fq)≠3. Our results answer a question of Davenport regarding the number of solutions of bounded height to x31+x32+x33=x34+x35+x36 with xi∈Fq[t].}, author = {Glas, Jakob and Hochfilzer, Leonhard}, booktitle = {arXiv}, title = {{On a question of Davenport and diagonal cubic forms over Fq(t)}}, doi = {10.48550/arXiv.2208.05422}, year = {2022}, } @article{7791, abstract = {Extending a result of Milena Radnovic and Serge Tabachnikov, we establish conditionsfor two different non-symmetric norms to define the same billiard reflection law.}, author = {Akopyan, Arseniy and Karasev, Roman}, issn = {2199-6768}, journal = {European Journal of Mathematics}, number = {4}, pages = {1309 -- 1312}, publisher = {Springer Nature}, title = {{When different norms lead to same billiard trajectories?}}, doi = {10.1007/s40879-020-00405-0}, volume = {8}, year = {2022}, } @article{8286, abstract = {We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor. }, author = {Alistarh, Dan-Adrian and Nadiradze, Giorgi and Sabour, Amirmojtaba}, issn = {1432-0541}, journal = {Algorithmica}, location = {Virtual, Online; Germany}, number = {4}, pages = {1007--1029}, publisher = {Springer Nature}, title = {{Dynamic averaging load balancing on cycles}}, doi = {10.1007/s00453-021-00905-9}, volume = {84}, year = {2022}, } @article{8538, abstract = {We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.}, author = {Akopyan, Arseniy and Schwartz, Richard and Tabachnikov, Serge}, issn = {2199-6768}, journal = {European Journal of Mathematics}, number = {4}, pages = {1313--1327}, publisher = {Springer Nature}, title = {{Billiards in ellipses revisited}}, doi = {10.1007/s40879-020-00426-9}, volume = {8}, year = {2022}, } @article{9199, abstract = {We associate a certain tensor product lattice to any primitive integer lattice and ask about its typical shape. These lattices are related to the tangent bundle of Grassmannians and their study is motivated by Peyre's programme on "freeness" for rational points of bounded height on Fano varieties.}, author = {Browning, Timothy D and Horesh, Tal and Wilsch, Florian Alexander}, issn = {1944-7833}, journal = {Algebra & Number Theory}, number = {10}, pages = {2385--2407}, publisher = {Mathematical Sciences Publishers}, title = {{Equidistribution and freeness on Grassmannians}}, doi = {10.2140/ant.2022.16.2385}, volume = {16}, year = {2022}, } @article{9311, abstract = {Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function. }, author = {Chatterjee, Krishnendu and Saona Urmeneta, Raimundo J and Ziliotto, Bruno}, issn = {1526-5471}, journal = {Mathematics of Operations Research}, keywords = {Management Science and Operations Research, General Mathematics, Computer Science Applications}, number = {1}, pages = {100--119}, publisher = {Institute for Operations Research and the Management Sciences}, title = {{Finite-memory strategies in POMDPs with long-run average objectives}}, doi = {10.1287/moor.2020.1116}, volume = {47}, year = {2022}, } @article{9336, abstract = {Mentorship is experience and/or knowledge‐based guidance. Mentors support, sponsor and advocate for mentees. Having one or more mentors when you seek advice can significantly influence and improve your research endeavours, well‐being and career development. Positive mentee–mentor relationships are vital for maintaining work–life balance and success in careers. Early‐career researchers (ECRs), in particular, can benefit from mentorship to navigate challenges in academic and nonacademic life and careers. Yet, strategies for selecting mentors and maintaining interactions with them are often underdiscussed within research environments. In this Words of Advice, we provide recommendations for ECRs to seek and manage mentorship interactions. Our article draws from our experiences as ECRs and published work, to provide suggestions for mentees to proactively promote beneficial mentorship interactions. The recommended practices highlight the importance of identifying mentorship needs, planning and selecting multiple and diverse mentors, setting goals, and maintaining constructive, and mutually beneficial working relationships with mentors.}, author = {Sarabipour, Sarvenaz and Hainer, Sarah J. and Arslan, Feyza N and De Winde, Charlotte M. and Furlong, Emily and Bielczyk, Natalia and Jadavji, Nafisa M. and Shah, Aparna P. and Davla, Sejal}, issn = {1742-4658}, journal = {FEBS Journal}, number = {6}, pages = {1374--1384}, publisher = {Wiley}, title = {{Building and sustaining mentor interactions as a mentee}}, doi = {10.1111/febs.15823}, volume = {289}, year = {2022}, } @article{9364, abstract = {Let t : Fp → C be a complex valued function on Fp. A classical problem in analytic number theory is bounding the maximum M(t) := max 0≤H

0 there exists a large subset of a ∈ F×p such that for kl a,1,p : x → e((ax+x) / p) we have M(kla,1,p) ≥ (1−ε/√2π + o(1)) log log p, as p→∞. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}a∈F×p. 2020 Mathematics Subject Classification: 11L03, 11T23 (Primary); 14F20, 60F10 (Secondary).}, author = {Bonolis, Dante}, issn = {1469-8064}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society}, number = {3}, pages = {563 -- 590}, publisher = {Cambridge University Press}, title = {{On the size of the maximum of incomplete Kloosterman sums}}, doi = {10.1017/S030500412100030X}, volume = {172}, year = {2022}, } @article{9365, abstract = {In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method.}, author = {Ogbuisi, Ferdinard U. and Shehu, Yekini and Yao, Jen Chih}, issn = {1029-4945}, journal = {Optimization}, number = {13}, pages = {3767--3795}, publisher = {Taylor and Francis}, title = {{Convergence analysis of new inertial method for the split common null point problem}}, doi = {10.1080/02331934.2021.1914035}, volume = {71}, year = {2022}, } @article{9469, abstract = {In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis.}, author = {Iyiola, Olaniyi S. and Enyi, Cyril D. and Shehu, Yekini}, issn = {1029-4937}, journal = {Optimization Methods and Software}, number = {4}, pages = {1527--1565}, publisher = {Taylor and Francis}, title = {{Reflected three-operator splitting method for monotone inclusion problem}}, doi = {10.1080/10556788.2021.1924715}, volume = {37}, year = {2022}, } @article{9649, abstract = {Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary.}, author = {Boissonnat, Jean-Daniel and Wintraecken, Mathijs}, issn = {1615-3383}, journal = {Foundations of Computational Mathematics }, pages = {967--1012}, publisher = {Springer Nature}, title = {{The topological correctness of PL approximations of isomanifolds}}, doi = {10.1007/s10208-021-09520-0}, volume = {22}, year = {2022}, } @article{9695, abstract = {Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using subsets of these features. Using the fewest features but still retaining sufficient information about the system is crucial in many statistical learning approaches, particularly when data are sparse. We introduce a statistical test that can assess the relative information retained when using two different distance measures, and determine if they are equivalent, independent, or if one is more informative than the other. This in turn allows finding the most informative distance measure out of a pool of candidates. The approach is applied to find the most relevant policy variables for controlling the Covid-19 epidemic and to find compact yet informative representations of atomic structures, but its potential applications are wide ranging in many branches of science.}, author = {Glielmo, Aldo and Zeni, Claudio and Cheng, Bingqing and Csanyi, Gabor and Laio, Alessandro}, issn = {2752-6542}, journal = {PNAS Nexus}, number = {2}, publisher = {Oxford University Press}, title = {{Ranking the information content of distance measures}}, doi = {10.1093/pnasnexus/pgac039}, volume = {1}, year = {2022}, } @article{9794, abstract = {Lymph nodes (LNs) comprise two main structural elements: fibroblastic reticular cells that form dedicated niches for immune cell interaction and capsular fibroblasts that build a shell around the organ. Immunological challenge causes LNs to increase more than tenfold in size within a few days. Here, we characterized the biomechanics of LN swelling on the cellular and organ scale. We identified lymphocyte trapping by influx and proliferation as drivers of an outward pressure force, causing fibroblastic reticular cells of the T-zone (TRCs) and their associated conduits to stretch. After an initial phase of relaxation, TRCs sensed the resulting strain through cell matrix adhesions, which coordinated local growth and remodeling of the stromal network. While the expanded TRC network readopted its typical configuration, a massive fibrotic reaction of the organ capsule set in and countered further organ expansion. Thus, different fibroblast populations mechanically control LN swelling in a multitier fashion.}, author = {Assen, Frank P and Abe, Jun and Hons, Miroslav and Hauschild, Robert and Shamipour, Shayan and Kaufmann, Walter and Costanzo, Tommaso and Krens, Gabriel and Brown, Markus and Ludewig, Burkhard and Hippenmeyer, Simon and Heisenberg, Carl-Philipp J and Weninger, Wolfgang and Hannezo, Edouard B and Luther, Sanjiv A. and Stein, Jens V. and Sixt, Michael K}, issn = {1529-2916}, journal = {Nature Immunology}, pages = {1246--1255}, publisher = {Springer Nature}, title = {{Multitier mechanics control stromal adaptations in swelling lymph nodes}}, doi = {10.1038/s41590-022-01257-4}, volume = {23}, year = {2022}, } @article{9955, abstract = {Neurons can change their classical neurotransmitters during ontogeny, sometimes going through stages of dual release. Here, we explored the development of the neurotransmitter identity of neurons of the avian nucleus isthmi parvocellularis (Ipc), whose axon terminals are retinotopically arranged in the optic tectum (TeO) and exert a focal gating effect upon the ascending transmission of retinal inputs. Although cholinergic and glutamatergic markers are both found in Ipc neurons and terminals of adult pigeons and chicks, the mRNA expression of the vesicular acetylcholine transporter, VAChT, is weak or absent. To explore how the Ipc neurotransmitter identity is established during ontogeny, we analyzed the expression of mRNAs coding for cholinergic (ChAT, VAChT, and CHT) and glutamatergic (VGluT2 and VGluT3) markers in chick embryos at different developmental stages. We found that between E12 and E18, Ipc neurons expressed all cholinergic mRNAs and also VGluT2 mRNA; however, from E16 through posthatch stages, VAChT mRNA expression was specifically diminished. Our ex vivo deposits of tracer crystals and intracellular filling experiments revealed that Ipc axons exhibit a mature paintbrush morphology late in development, experiencing marked morphological transformations during the period of presumptive dual vesicular transmitter release. Additionally, although ChAT protein immunoassays increasingly label the growing Ipc axon, this labeling was consistently restricted to sparse portions of the terminal branches. Combined, these results suggest that the synthesis of glutamate and acetylcholine, and their vesicular release, is complexly linked to the developmental processes of branching, growing and remodeling of these unique axons.}, author = {Reyes‐Pinto, Rosana and Ferrán, José L. and Vega Zuniga, Tomas A and González‐Cabrera, Cristian and Luksch, Harald and Mpodozis, Jorge and Puelles, Luis and Marín, Gonzalo J.}, issn = {1096-9861}, journal = {Journal of Comparative Neurology}, number = {2}, pages = {553--573}, publisher = {Wiley}, title = {{Change in the neurochemical signature and morphological development of the parvocellular isthmic projection to the avian tectum}}, doi = {10.1002/cne.25229}, volume = {530}, year = {2022}, } @article{9977, abstract = {For a Seifert fibered homology sphere X we show that the q-series invariant Zˆ0(X; q) introduced by Gukov-Pei-Putrov-Vafa, is a resummation of the Ohtsuki series Z0(X). We show that for every even k ∈ N there exists a full asymptotic expansion of Zˆ0(X; q) for q tending to e 2πi/k, and in particular that the limit Zˆ0(X; e 2πi/k) exists and is equal to the WRT quantum invariant τk(X). We show that the poles of the Borel transform of Z0(X) coincide with the classical complex Chern-Simons values, which we further show classifies the corresponding components of the moduli space of flat SL(2, C)-connections.}, author = {Mistegaard, William and Andersen, Jørgen Ellegaard}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {2}, pages = {709--764}, publisher = {Wiley}, title = {{Resurgence analysis of quantum invariants of Seifert fibered homology spheres}}, doi = {10.1112/jlms.12506}, volume = {105}, year = {2022}, } @article{22043, abstract = {We prove that multisoliton solutions of the Korteweg–de Vries equation are orbitally stable in H^-1(R). We introduce a variational characterization of multisolitons that remains meaningful at such low regularity and show that all optimizing sequences converge to the manifold of multisolitons. The proximity required at the initial time is uniform across the entire manifold of multisolitons; this had not been demonstrated previously, even in H^-1.}, author = {Killip, Rowan and Visan, Monica}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {1445--1473}, publisher = {Springer Nature}, title = {{Orbital stability of KdV multisolitons in H-1}}, doi = {10.1007/s00220-021-04280-y}, volume = {389}, year = {2022}, }