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Rigid matrices from rectangular PCPs
No full textWe introduce a variant of Probabilistically Checkable Proofs (PCPs) that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each query and the other determining the column. We construct PCPs that are efficient, short, smooth, and (almost) rectangular. As a key application, we show that proofs for hard languages in NTIME (2n), when viewed as matrices, are rigid infinitely often. This strengthens and simplifies a recent result of Alman and Chen [FOCS, 2019] constructing explicit rigid matrices in FNP. Namely, we prove the following theorem: There is a constant δ ∈ (0, 1)such that there is an FNP-machine that, for infinitely many N, on input 1N outputs N x N matrices with entries in F2 that are δN2-far (in Hamming distance) from matrices of rank at most 2log N/Ω(log log N). Our construction of rectangular PCPs starts with an analysis of how randomness yields queries in the Reed–Muller-based outer PCP of Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan. We then show how to preserve rectangularity under PCP composition and a smoothness-inducing transformation. This warrants refined and stronger notions of rectangularity, which we prove for the outer PCP and its transforms
An improved line-point low-degree test*
No full textWe prove that the most natural low-degree test for polynomials over finite fields is "robust" in the high-error regime for linear-sized fields. Specifically we consider the “local” agreement of a function f:Fmq→Fq from the space of degree-d polynomials, i.e., the expected agreement of the function from univariate degree-d polynomials over a randomly chosen line in Fmq, and prove that if this local agreement is ε≥Ω((d/q)τ)) for some fixed τ>0, then there is a global degree-d polynomial Q:mq→Fq with agreement nearly ε with f. This settles a long-standing open question in the area of low-degree testing, yielding an O(d) -query robust test in the “high-error” regime (i.e., when ε<1/2). The previous results in this space either required ε>1/2 (Polishchuk & Spielman, STOC 1994), or q=Ω(d4) (Arora & Sudan, Combinatorica 2003), orneeded to measure local distance on 2-dimensional “planes” rather than one-dimensional lines leading to Ω(d2) -query complexity (Raz & Safra, STOC 1997). Our analysis follows the spirit of most previous analyses in first analyzing the low-variable case (m=O(1)) and then “boot-strapping” to general multivariate settings. Our main technical novelty is a new analysis in the bivariate setting that exploits a previously known connection between multivariate factorization and finding (or testing) low-degree polynomials, in a non “black-box” manner. This connection was used roughly in a black-box manner in the work of Arora & Sudan — and we show that opening up this black box and making some delicate choices in the analysis leads to our essentially optimal analysis. A second contribution is a bootstrapping analysis which manages to lift analyses for m=2 directly to analyses for general m, where previous works needed to work with m=3 or m=4 — arguably this bootstrapping is significantly simpler than those in prior works
What do we see behind an occluder? Amodal completion of statistical properties in complex objects
No full textWhen a spiky object is occluded, we expect its spiky features to continue behind the occluder. Although many real-world objects contain complex features, it is unclear how more complex features are amodally completed and whether this process is automatic. To investigate this issue, we created pairs of displays with identical contour edges up to the point of occlusion, but with occluded portions exchanged. We then asked participants to search for oddball targets among distractors and asked whether relations between searches involving occluded displays would match better with relations between searches involving completions that are either globally consistent or inconsistent with the visible portions of these displays. Across two experiments involving simple and complex shapes, search times involving occluded displays matched better with those involving globally consistent compared with inconsistent displays. Analogous analyses on deep networks pretrained for object categorization revealed a similar pattern of results for simple but not complex shapes. Thus, deep networks seem to extrapolate simple occluded contours but not more complex contours. Taken together, our results show that amodal completion in humans is sophisticated and can be based on extrapolating global statistical properties
Cell shape affects bacterial colony growth under physical confinement
No full textEvidence from homogeneous liquid or flat-plate cultures indicates that biochemical cues are the primary modes of bacterial interaction with their microenvironment. However, these systems fail to capture the effect of physical confinement on bacteria in their natural habitats. Bacterial niches like the pores of soil, mucus, and infected tissues are disordered microenvironments with material properties defined by their internal pore sizes and shear moduli. Here, we use three-dimensional matrices that match the viscoelastic properties of gut mucus to test how altering the physical properties of their microenvironment influences the growth of bacteria under confinement. We find that low aspect ratio (spherical) bacteria form compact, spherical colonies under confinement while high aspect ratio (rod-shaped) bacteria push their progenies further outwards to create elongated colonies with a higher surface area, enabling increased access to nutrients. As a result, the population growth of high aspect ratio bacteria is, under the tested conditions, more robust to increased physical confinement compared to that of low aspect ratio bacteria. Thus, our experimental evidence supports that environmental physical constraints can play a selective role in bacterial growth based on cell shape
Mutational Signatures in Wild Type <i>Escherichia coli</i> Strains Reveal Predominance of DNA Polymerase Errors
No full textWhile mutational processes operating in the Escherichia coli genome have been revealed by multiple laboratory experiments, the contribution of these processes to accumulation of bacterial polymorphism and evolution in natural environments is unknown. To address this question, we reconstruct signatures of distinct mutational processes from experimental data on E. coli hypermutators, and ask how these processes contribute to differences between naturally occurring E. coli strains. We show that both mutations accumulated in the course of evolution of wild-type strains in nature and in the lab-grown nonmutator laboratory strains are explained predominantly by the low fidelity of DNA polymerases II and III. By contrast, contributions specific to disruption of DNA repair systems cannot be detected, suggesting that temporary accelerations of mutagenesis associated with such disruptions are unimportant for within-species evolution. These observations demonstrate that accumulation of diversity in bacterial strains in nature is predominantly associated with errors of DNA polymerases
Induction thermography for unidirectional CFRP composites: A novel inspection approach through global current path integration
No full textIn the evolving field of non-destructive testing of composite materials, induction thermography offers significant potential. However, its application to Unidirectional Carbon Fiber Reinforced Polymer (UD CFRP) composites remains challenging due to the unavailability of global current paths. This study introduces a novel methodology to inspect UD CFRP composites using Induction Thermography by incorporating an additional conduction current loop between the composite layers. Initial proof-of-concept experiments were conducted on fiber tow and further validated on laminates. The findings substantiate that the integration of a global current path notably facilitates laminate heating, enhancing the induction thermographic inspection capability. An unexpected discovery in our research is the ability of a circular coil to detect fiber breakage in a laminate that is nearly an order of magnitude wider than the coil diameter, thus demonstrating the approach’s high sensitivity. The practical applicability of the proposed methodology was demonstrated using an external fixture. Moreover, this work proposes an innovative modification to the manufacturing process of non-crimp textiles by incorporating a conductive thread, envisaged to bolster the induction thermographic inspection efficiency further. Numerical modeling, closely aligning with experimental observations, provides a robust theoretical foundation for our work
Recent Indian studies in Himalayan cryosphere
No full textCryosphere all over the globe is thawing, be it the Arctic, Antarctic, Greenland or Himalaya. Studies have predicted that loss in the glacier mass over the Upper Indus Basin in Kashmir Himalaya would amount to 47 to 67% (Romshoo in 7th conference of Science and Geopolitics of Arctic and Antarctic, 2023). A similar trend prevails in the Bhaga basin of the Upper Chenab, where glaciers in size classes < 0.5 km2 and 0.5-1 km2 show a higher relative loss of 25% (0.5% year-1) and 13% (0.3% year-1) respectively (Das et al. in Quat Sci Rev 316:108258; J Mt Sci 20:299–324, 2023). The loss in Eastern Himalaya (Sikkim) has been reported to range from 20 to 30% (Debnath in 7th conference of Science and Geopolitics of Arctic and Antarctic, 2023). On the basis of the compiled records of snout fluctuations of 285 glaciers and two regional means spanning 17 decades from the 1850s, it has been deduced that most of the Himalayan glaciers are retreating, and the retreat rates have accelerated in the past few decades, but the observed tendencies are not regionally uniform (Kulkarni et al. in Water Security 14(6557):100101; J Indian Soc Remote Sensing 49(8):1951–1963, 2021). The excessive ice mass loss has resulted in the formation and/or expansion of glacial melt water lakes posing a threat of Glacial Lake Outburst Flow (GLOF). The results of the studies on the response of climatic variability over the state of cryosphere, the role of debris on the melting of glaciers, changes in the winter precipitation pattern and consequent impact on the hydrological cycle, water availability and state of permafrost over Himalaya have also been a focus of studies, including developing models (Banerjee et al. in Geophys Res Lett 49:096989, 2020), in contemporary publications, enriching the data on the fundamental aspects of glacial processes that are of great societal relevance
Himalayan Re-gridded and Observational Experiment (HiROX): Part II – Application
No full textThis paper releases two regional precipitation products produced in the Himalayan Re-gridded and Observational Experiment (HiROX) conducted over the Central (Uttarakhand) Himalayas including the Upper Ganga Basin. The distributed precipitation products cover a period of about 70 yrs: HiROX-1 ranges from 1972 to 2018 (47 yrs) and is a regridded static daily precipitation product, and HiROX-2 ranges from 2000 to 2021 (22 yrs) and is a regridded dynamic daily precipitation product with continuous upgradation capacity. These datasets are capable of (a) precisely capturing and reproducing refined spatial distribution of precipitation and (b) preserving data accuracy along with other spatiotemporal characteristics over the study region, better than that observed in popular precipitation products covering the study region. The comparative investigation established HiROX-1 as better than some or all the tested datasets in terms of (a) spatial resolution, (b) accuracy, (c) temporal resolution, (d) temporal coverage, and (e) spatial distribution, and presents their application suitability. The second precipitation product, HiROX-2, closely followed HiROX-1, as reported in the ensuing investigation. We employed an open-source precipitation model, HiROX-M1, a flexible machine learning framework capable of processing precipitation information at fine spatial resolution. These regional precipitation products are provided at a spatial resolution of 5 × 5 km2 on daily scale over projected and geographic coordinate systems. HiROX-1 is a station-dependent product and HiROX-2 is a near real-time station-independent product with an updated frequency equal to that of Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG) Final Precipitation L3 1 day 0.1° × 0.1° V06 (GPM_3IMERGDF V06) product. The released products are platform-independent in choice of operating system and geographic information system (GIS) interface. The released data shall assist in closing the spatial discontinuity of ground station information over the Central Himalayan region over Uttarakhand, including the Upper Ganga Basi
Multiparametric flow cytometry in the evaluation of plasma cell proliferative disorders: Current paradigms for clinical practice
No full textDiagnosis of plasma cell proliferative disorders (PCPDs) is primarily based on the demonstration of monoclonal protein (M-Protein) in blood and/ or urine which often precedes clinical manifestations of the disease. The basic pathophysiology behind the M-protein presence is the proliferation of clonal plasma cells (PCs) in bone marrow or extramedullary sites and is assessed using cytomorphology and immunophenotyping. The role of multiparametric flow cytometry (MFC) for PC identification is technically the most valuable tool in this context as it characterizes as well as quantifies the clonal PCs based on differential expression of various immunophenotypic (IPT) markers. From a diagnostic perspective, MFC is critical in the definite identification of the clonal PCs and delineates benign and borderline entities at one end of the spectrum (MGUS, SMM) with lower clonal PC% and, malignant diseases at the other end (MM and PCL) with higher clonal PC fraction. The role of MFC in assessment of measurable residual disease (MRD) and monitoring of progression in MM and various PCPDs has been validated in multiple clinical studies and is probably one of the most promising tools for predicting treatment outcomes. Furthermore, MFC also plays a crucial role in disease prognostication based on specific IPT profiles. An additional role of MFC in the current clinical scenario is the evaluation of tumor microenvironment based on immune cell repertoire, which is reflecting encouraging results across. Thus, in the current review we concisely describe the role of MFC as a reliable and essential modality in PCPDs, from diagnosis to prediction of treatment outcome and disease monitoring
Entropy‐Driven Reversible Melting and Recrystallization of Layered Hybrid Perovskites
No full textTypical layered 2D A2PbX4 (A: organic ammonium cation, X: Br, I) perovskites undergo irreversible decomposition at high temperatures. Can they be designed to melt at lower temperatures without decomposition? Which thermodynamic parameter drive the melting of layered perovskites? These questions are addressed by considering the melt of A2PbX4 as a mixture of ions (like ionic liquids), and hypothesized that the increase in the structural entropy of fusion (ΔSfus) will be the driving force to decrease their melting temperature. Then to increase structural ΔSfus, A-site cations are designed that are rigid in the solid crystal, and become flexible in the molten state. Different tail groups in the A-site cations form hydrogen-, halogen- and even covalent bonding-interactions, making the cation-layer rigid in the solid form. Additionally, the rotation of ─NH3+ head group is suppressed by replacing ─H with ─CH3, further enhancing the rigidity. Six A2PbX4 crystals with high ΔSfus and low melting temperatures are prepared using this approach. For example, [I−(CH2)3−NH2 (CH3)]2PbI4 reversibly melts at 388 K (decomposition temperature 500 K), and then recrystallizes back upon cooling. Consequently, melt-pressed films are grown demonstrating the solvent- and vacuum-free perovskite films for future optoelectronic device