On Polynomial Time Constructions of Minimum Height Decision Tree

A decision tree T in B_m:={0,1}^m is a binary tree where each of its internal nodes is labeled with an integer in [m]={1,2,...,m}, each leaf is labeled with an assignment a in B_m and each internal node has two outgoing edges that are labeled with 0 and 1, respectively. Let A subset {0,1}^m. We say that T is a decision tree for A if (1) For every a in A there is one leaf of T that is labeled with a. (2) For every path from the root to a leaf with internal nodes labeled with i_1,i_2,...,i_k in[m], a leaf labeled with a in A and edges labeled with xi_{i_1},...,xi_{i_k}in {0,1}, a is the only element in A that satisfies a_{i_j}=xi_{i_j} for all j=1,...,k. Our goal is to write a polynomial time (in n:=|A| and m) algorithm that for an input A subseteq B_m outputs a decision tree for A of minimum depth. This problem has many applications that include, to name a few, computer vision, group testing, exact learning from membership queries and game theory. Arkin et al. and Moshkov [Esther M. Arkin et al., 1998; Mikhail Ju. Moshkov, 2004] gave a polynomial time (ln |A|)- approximation algorithm (for the depth). The result of Dinur and Steurer [Irit Dinur and David Steurer, 2014] for set cover implies that this problem cannot be approximated with ratio (1-o(1))* ln |A|, unless P=NP. Moshkov studied in [Mikhail Ju. Moshkov, 2004; Mikhail Ju. Moshkov, 1982; Mikhail Ju. Moshkov, 1982] the combinatorial measure of extended teaching dimension of A, ETD(A). He showed that ETD(A) is a lower bound for the depth of the decision tree for A and then gave an exponential time ETD(A)/log(ETD(A))-approximation algorithm and a polynomial time 2(ln 2)ETD(A)-approximation algorithm. In this paper we further study the ETD(A) measure and a new combinatorial measure, DEN(A), that we call the density of the set A. We show that DEN(A) <=ETD(A)+1. We then give two results. The first result is that the lower bound ETD(A) of Moshkov for the depth of the decision tree for A is greater than the bounds that are obtained by the classical technique used in the literature. The second result is a polynomial time (ln 2)DEN(A)-approximation (and therefore (ln 2)ETD(A)-approximation) algorithm for the depth of the decision tree of A. We then apply the above results to learning the class of disjunctions of predicates from membership queries [Nader H. Bshouty et al., 2017]. We show that the ETD of this class is bounded from above by the degree d of its Hasse diagram. We then show that Moshkov algorithm can be run in polynomial time and is (d/log d)-approximation algorithm. This gives optimal algorithms when the degree is constant. For example, learning axis parallel rays over constant dimension space

Enhanced taupathy and AD-like pathology in aged primate brains decades after infantile exposure to lead (Pb)

Late Onset Alzheimer Disease (LOAD) constitutes the majority of AD cases (∼90%). Amyloidosis and tau pathology, which are present in AD brains, appear to be sporadic in nature. We have previously shown that infantile lead (Pb) exposure is associated with a change in the expression and regulation of the amyloid precursor protein (APP) and its beta amyloid (Aβ) products in old age. Here we report that infantile Pb exposure elevated the mRNA and protein levels of tau as well as its transcriptional regulators namely specificity protein 1 and 3 (Sp1 and Sp3) in aged primates. These changes were also accompanied by an enhancement in site-specific tau phosphorylation as well as an increase in the mRNA and protein levels of cyclin dependent kinase 5 (cdk5). There was also a change in the protein ratio of p35/p25 with more Serine/Threonine phosphatase activity present in aged primates exposed to Pb as infants. These molecular alterations favored abundant tau phosphorylation and immunoreactivity in the frontal cortex of aged primates with prior Pb exposure. These findings provide more evidence that neurodegenerative diseases may be products of environmental influences that occur during the development

Evolution of Fermion Pairing from Three to Two Dimensions

We follow the evolution of fermion pairing in the dimensional crossover from 3D to 2D as a strongly interacting Fermi gas of $^6$Li atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice. Decreasing the dimensionality leads to the opening of a gap in radio-frequency spectra, even on the BCS-side of a Feshbach resonance. The measured binding energy of fermion pairs closely follows the theoretical two-body binding energy and, in the 2D limit, the zero-temperature mean-field BEC-BCS theory.Comment: 5 pages, 4 figure

Unusual Behavior in Children-Foreign Object in Tooth: A Report of Two Cases

Background: The chance of discovering foreign object in a root canal is more commonly seen in children. Foreign objects may act as a potential source of infection, which may hinder the complete debridement of root canal. Although the main etiology being an accidental insertion, there are other possibilities such as self-injurious habits which should be ruled out.Case Details: The present article describes two case of foreign object in root canal, their possible etiology and management modalities. The first case reports a usual case of staple pin in root canal of primary teeth. The second case was a broken pin inside anterior permanent teeth. The cases reported highlight the need for proper diagnosis and early management.Conclusion: This case report highlights the need for proper understanding of the etiology in management of foreign body in root canal system.Keywords: Foreign object, Self-Embedding habit, Stapler pi

Mechanical properties of P/M refractory high entropy alloys

The mechanical properties of refractory high entropy alloys are investigated to develop advanced heat-resistant alloys for high-temperature structural applications. The alloy systems were selected to have multi-principal refractory elements including, tungsten, molybdenum, niobium, vanadium, tantalum, and titanium. Mechanical alloying and spark plasma sintering were used to fabricate the WMoNbV(Ta,Ti) samples to characterize the microstructure and mechanical properties. Through powder metallurgy (P/M) processing, more precise control of compositions was possible. Crystalline structures and lattice parameters before and after sintering were measured by X-ray diffraction, and the sizes and compositions of multiple phases were measured by scanning electron microscopy, energy-dispersive x-ray spectroscopy, and transmission electron microscopy. When compared with the reported grain size of cast refractory high entropy alloys, the average grain size of P/M refractory high entropy alloys was significantly smaller. At room temperature, the Vickers hardness and the yield strength of P/M refractory high entropy alloys were much superior to those of cast refractory high entropy alloys. The compressive yield strength of WMoNbV(Ta,Ti) ranged from 2 to 3.6 GPa with a fracture strain of 9.7 %. The previously reported compressive yield strength was 1.2 GPa with a very limited strain for cast high entropy alloys with similar compositions. The elevated temperature compressive yield strength was also enhanced in the P/M WMoNbV(Ta,Ti) alloys. Increased compressive yield strength of approximately 1 GPa was measured at 1000oC. Fine-structured multi-phases with solid solution hardening were attributed to the improved mechanical properties of P/M refractory high entropy alloys

Infantile postnatal exposure to lead (Pb) enhances tau expression in the cerebral cortex of aged mice: Relevance to AD

The sporadic nature in over 90% of Alzheimer\u27s disease (AD) cases, the differential susceptibility and course of illness, and latent onset of the disease suggest involvement of an environmental component in the etiology of late onset AD (LOAD). Recent reports from our lab have demonstrated that molecular alterations favor abundant tau phosphorylation and immunoreactivity in the frontal cortex of aged primates with infantile lead (Pb) exposure (Bihaqi and Zawia, 2013). Here we report that developmental Pb exposure results in elevation of protein and mRNA levels of tau in aged mice. Western blot analysis revealed aberrant site-specific tau hyperphosphorylation accompanied by elevated cyclin dependent kinase 5 (CDK5) levels in aged mice with prior Pb exposure. Mice with developmental Pb exposure also displayed altered protein ratio of p35/p25 with more Serine/Threonine phosphatase activity at old age. These changes favored increase in tau phosphorylation, thus providing evidence that neurodegenerative diseases may be in part due to environmental influences that occur during development

Revisiting the mechanistic pathways for bacterial mediated synthesis of noble metal nanoparticles

Synthesis and application of reliable nanoscale materials is a progressive domain and the limelight of modern nanotechnology. Conventional physicochemical approaches for the synthesis of metal nanoparticles have become obsolete owing to costly and hazardous materials. There is a need to explore alternative, cost-effective and eco-friendly strategies for fabrication of nanoparticle (NPs). Green synthesis of noble metal nanoparticles has emerged as a promising approach in the last decade. Elucidation of the molecular mechanism is highly essential in the biological synthesis of noble metal nanoparticles (NPs) for the controlled size, shape, and monodispersity. Moreover, mechanistic insights will help to scale up the facile synthesis protocols and will enable biotransformation of toxic heavy metals hence also providing the detoxification effects. Therefore, the current review article has primarily targeted the mechanisms involved in the green synthesis of metal NPs, which have been reported during the last few years. Detailed mechanistic pathways have highlighted nitrate reductase as a principle reducing agent in the bacterial mediated synthesis and stabilization of NPs. Furthermore, we have highlighted the potential implications of these mechanisms in bioremediation and biomineralization processes, which can play a critical role in biogeochemical cycling and environmental impacts of heavy metals. We anticipate that this review article will help researchers to address the challenges of bioremediation and modern nanotechnology

A Unified Approach towards Describing Rapidity and Transverse Momentum Distributions in Thermal Freeze-Out Model

We have attempted to describe the rapidity and transverse momentum spectra, simultaneously, of the hadrons produced in the Ultra-relativistic Nuclear Collisions. This we have tried to achieve in a single statistical thermal freeze-out model using single set of parameters. We assume the formation of a hadronic gas in thermo-chemical equilibrium at the freeze-out. The model incorporates a longitudinal as well as a transverse hydrodynamic flow. We have also found that the role of heavier hadronic resonance decay is important in explaining the particle spectra.Comment: 22 pages, 11 figure

Impact of N-Terminal Tags on De Novo Vimentin Intermediate Filament Assembly

Vimentin, a type III intermediate filament protein, is found in most cells along with microfilaments and microtubules. It has been shown that the head domain folds back to associate with the rod domain and this association is essential for filament assembly. The N-terminally tagged vimentin has been widely used to label the cytoskeleton in live cell imaging. Although there is previous evidence that EGFP tagged vimentin fails to form filaments but is able to integrate into a pre-existing network, no study has systematically investigated or established a molecular basis for this observation. To determine whether a tag would affect de novo filament assembly, we used vimentin fused at the N-terminus with two different sized tags, AcGFP (239 residues, 27 kDa) and 3 × FLAG (22 residues; 2.4 kDa) to assemble into filaments in two vimentin-deficient epithelial cells, MCF-7 and A431. We showed that regardless of tag size, N-terminally tagged vimentin aggregated into globules with a significant proportion co-aligning with β-catenin at cell–cell junctions. However, the tagged vimentin aggregates could form filaments upon adding untagged vimentin at a ratio of 1:1 or when introduced into cells containing pre-existing filaments. The resultant filament network containing a mixture of tagged and untagged vimentin was less stable compared to that formed by only untagged vimentin. The data suggest that placing a tag at the N-terminus may create steric hinderance in case of a large tag (AcGFP) or electrostatic repulsion in case of highly charged tag (3 × FLAG) perhaps inducing a conformational change, which deleteriously affects the association between head and rod domains. Taken together our results shows that a free N-terminus is essential for filament assembly as N-terminally tagged vimentin is not only incapable of forming filaments, but it also destabilises when integrated into a pre-existing network