Superpolynomial lower bounds for general homogeneous depth 4 arithmetic circuits

In this paper, we prove superpolynomial lower bounds for the class of homogeneous depth 4 arithmetic circuits. We give an explicit polynomial in VNP of degree $n$ in $n^2$ variables such that any homogeneous depth 4 arithmetic circuit computing it must have size $n^{\Omega(\log \log n)}$. Our results extend the works of Nisan-Wigderson [NW95] (which showed superpolynomial lower bounds for homogeneous depth 3 circuits), Gupta-Kamath-Kayal-Saptharishi and Kayal-Saha-Saptharishi [GKKS13, KSS13] (which showed superpolynomial lower bounds for homogeneous depth 4 circuits with bounded bottom fan-in), Kumar-Saraf [KS13a] (which showed superpolynomial lower bounds for homogeneous depth 4 circuits with bounded top fan-in) and Raz-Yehudayoff and Fournier-Limaye-Malod-Srinivasan [RY08, FLMS13] (which showed superpolynomial lower bounds for multilinear depth 4 circuits). Several of these results in fact showed exponential lower bounds. The main ingredient in our proof is a new complexity measure of {\it bounded support} shifted partial derivatives. This measure allows us to prove exponential lower bounds for homogeneous depth 4 circuits where all the monomials computed at the bottom layer have {\it bounded support} (but possibly unbounded degree/fan-in), strengthening the results of Gupta et al and Kayal et al [GKKS13, KSS13]. This new lower bound combined with a careful "random restriction" procedure (that transforms general depth 4 homogeneous circuits to depth 4 circuits with bounded support) gives us our final result

Inductor based switching DC-DC converter for low voltage power distribution in SLHC

In view of a power distribution scheme compatible with the requirements of the SLHC environment, we are evaluating the feasibility of on-board inductor-based DC-DC step-down conversion. Such converter should be an integrated circuit and capable of operating in harsh radiation environments and in the high magnetic field of the experiments. In this paper we present results concerning the choice of the technology, the search for the magnetic components and the calculations of the expected efficiency

On higher multiplicity hyperplane and polynomial covers for symmetry preserving subsets of the hypercube

Alon and F\"uredi (European J. Combin. 1993) gave a tight bound for the following hyperplane covering problem: find the minimum number of hyperplanes required to cover all points of the n-dimensional hypercube {0,1}^n except the origin. Their proof is among the early instances of the polynomial method, which considers a natural polynomial (a product of linear factors) associated to the hyperplane arrangement, and gives a lower bound on its degree, whilst being oblivious to the (product) structure of the polynomial. Thus, their proof gives a lower bound for a weaker polynomial covering problem, and it turns out that this bound is tight for the stronger hyperplane covering problem. In a similar vein, solutions to some other hyperplane covering problems were obtained, via solutions of corresponding weaker polynomial covering problems, in some special cases in the works of the fourth author (Electron. J. Combin. 2022), and the first three authors (Discrete Math. 2023). In this work, we build on these and solve a hyperplane covering problem for general symmetric sets of the hypercube, where we consider hyperplane covers with higher multiplicities. We see that even in this generality, it is enough to solve the corresponding polynomial covering problem. Further, this seems to be the limit of this approach as far as covering symmetry preserving subsets of the hypercube is concerned. We gather evidence for this by considering the class of blockwise symmetric sets of the hypercube (which is a strictly larger class than symmetric sets), and note that the same proof technique seems to only solve the polynomial covering problem

Preferential Myosin Heavy Chain Isoform B Expression May Contribute to the Faster Velocity of Contraction in Veins versus Arteries

Smooth muscle myosin heavy chains occur in 2 isoforms, SMA (slow) and SMB (fast). We hypothesized that the SMB isoform is predominant in the faster-contracting rat vena cava compared to thoracic aorta. We compared the time to half maximal contraction in response to a maximal concentration of endothelin-1 (ET-1; 100 nM), potassium chloride (KCl; 100 mM) and norepinephrine (NE; 10 µM). The time to half maximal contraction was shorter in the vena cava compared to aorta (aorta: ET-1 = 235.8 ± 13.8 s, KCl = 140.0 ± 33.3 s, NE = 19.8 ± 2.7 s; vena cava: ET-1 = 121.8 ± 15.6 s, KCl = 49.5 ± 6.7 s, NE = 9.0 ± 3.3 s). Reverse-transcription polymerase chain reaction supported the greater expression of SMB in the vena cava compared to aorta. SMB was expressed to a greater extent than SMA in the vessel wall of the vena cava. Western analysis determined that expression of SMB, relative to total smooth muscle myosin heavy chains, was 12.5 ± 4.9-fold higher in the vena cava compared to aorta, while SMA was 4.9 ± 1.2-fold higher in the aorta than vena cava. Thus, the SMB isoform is the predominant form expressed in rat veins, providing one possible mechanism for the faster response of veins to vasoconstrictors

Seismotectonics of the 2001 Bhuj earthquake (Mw 7.7) in western India: Constraints from aftershocks

ABSTRACT More than 500 aftershocks (M > 2.0) are relocated to study the source processes of the January 26, 2001 Bhuj earthquake (M W 7.7) in western part of the peninsular Indian shield. The maximum intensity reached to X on the MSK scale, but no primary surface rupture or fault was mapped. The aftershocks are relocated by simultaneous inversion with an average rms of 0.19s, and average error estimates of latitude, longitude and depth are 1.2 km, 1.1 km and 2.3 km, respectively. Most of the aftershocks occurred in an area of 70 x 35 sq km; the maximum activity was observed at a depth range of 12-37 km. A bimodal distribution of aftershocks indicates that the main shock rupture propagated both in the upward and downward directions. Further, the best located larger magnitude aftershocks show two trends, one in northeast, parallel to the isoseismal trend and to the major Anjar Rapar Lineament/Delhi -Aravalli trend, and the other in northwest parallel to the Bhachau Lineament and a 8 km long secondary rupture. Fault-plane solutions of the northeast trending aftershocks indicate reverse faulting with left-lateral strike-slip motion; these are comparable to the main shock mechanism. The northwest trending aftershocks, on the other hand, show reverse faulting with right-lateral strike-slip motion. 3D-velocity, gravity, magnetic, ground positioning system (GPS) and satellite observations suggest block uplift during the main shock. These observations are comparable to the earthquake locations and source mechanisms of the main shock and aftershocks

Multi-epoch hard X-ray view of Compton-thick AGN Circinus Galaxy

The circumnuclear material around Active Galactic Nuclei (AGN) is one of the essential components of the obscuration-based unification model. However, our understanding of the circumnuclear material in terms of its geometrical shape, structure and its dependence on accretion rate is still debated. In this paper, we present the multi-epoch broadband X-ray spectral modelling of a nearby Compton-thick AGN in Circinus galaxy. We utilise all the available hard X-ray ($> 10$ keV) observations taken from different telescopes, $i.e.,$ $BeppoSAX$, $Suzaku$, $NuSTAR$ and $AstroSat$, at ten different epochs across $22$ years from $1998$ to $2020$. The $3.0-79$ keV broadband X-ray spectral modelling using physically-motivated models, namely MYTORUS, BORUS02 and UXCLUMPY, infers the presence of a torus with a low covering factor of $0.28$, an inclination angle of $77^{\circ}$ $-$ $81^{\circ}$ and Compton-thick line-of-sight column densities ($N_{\rm H,LOS} = 4.13~-~9.26~\times~10^{24}$ cm$^{-2}$) in all the epochs. The joint multi-epoch spectral modelling suggests that the overall structure of the torus is likely to remain unchanged. However, we find tentative evidence for the variable line-of-sight column density on timescales ranging from one day to one week to a few years, suggesting a clumpy circumnuclear material located at sub-parsec to tens of parsec scales.Comment: 18 pages, 7 figures, 6 tables, accepted for publication in Monthly Notices of the Royal Astronomical Societ

Accumulation of Immature Langerhans Cells in Human Lymph Nodes Draining Chronically Inflamed Skin

The coordinated migration and maturation of dendritic cells (DCs) such as intraepithelial Langerhans cells (LCs) is considered critical for T cell priming in response to inflammation in the periphery. However, little is known about the role of inflammatory mediators for LC maturation and recruitment to lymph nodes in vivo. Here we show in human dermatopathic lymphadenitis (DL), which features an expanded population of LCs in one draining lymph node associated with inflammatory lesions in its tributary skin area, that the Langerin/CD207+ LCs constitute a predominant population of immature DCs, which express CD1a, and CD68, but not CD83, CD86, and DC–lysosomal-associated membrane protein (LAMP)/CD208. Using LC-type cells generated in vitro in the presence of transforming growth factor (TGF)-β1, we further found that tumor necrosis factor (TNF)-α, as a prototype proinflammatory factor, and a variety of inflammatory stimuli and bacterial products, increase Langerin expression and Langerin dependent Birbeck granules formation in cell which nevertheless lack costimulatory molecules, DC–LAMP/CD208 and potent T cell stimulatory activity but express CCR7 and respond to the lymph node homing chemokines CCL19 and CCL21. This indicates that LC migration and maturation can be independently regulated events. We suggest that during DL, inflammatory stimuli in the skin increase the migration of LCs to the lymph node but without associated maturation. Immature LCs might regulate immune responses during chronic inflammation

Ground motion parameters in Shillong and Mikir Plateau supplemented by mapping of amplification factors in Guwahati City, Northeastern India

Ground motion parameters for Shillong–Mikir Plateau of Northeastern India are examined. Empirical relations are obtained for ground motions as a function of earthquake magnitude, fault type, source depth, velocity characterization of medium and distance. Correlation between ground motion parameters and characteristics of seismogenic zones are established. Simultaneously, new empirical relations are derived for attenuation of ground motion amplitudes. Correlation coefficients of the attenuation relations depend on the site classifications that are identified based on average shear wave velocity and site response factors. The attenuation relation estimated for logarithmic width of Mikir Plateau found to be a little bit higher than that of Shillong Plateau both for soft and hard groun