Quantified Derandomization of Linear Threshold Circuits

One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing approach to prove such lower bounds is to construct a non-trivial derandomization algorithm for $TC^0$. In this work we take a first step towards the latter goal, by proving the first positive results regarding the derandomization of $TC^0$ circuits of depth $d>2$. Our first main result is a quantified derandomization algorithm for $TC^0$ circuits with a super-linear number of wires. Specifically, we construct an algorithm that gets as input a $TC^0$ circuit $C$ over $n$ input bits with depth $d$ and $n^{1+\exp(-d)}$ wires, runs in almost-polynomial-time, and distinguishes between the case that $C$ rejects at most $2^{n^{1-1/5d}}$ inputs and the case that $C$ accepts at most $2^{n^{1-1/5d}}$ inputs. In fact, our algorithm works even when the circuit $C$ is a linear threshold circuit, rather than just a $TC^0$ circuit (i.e., $C$ is a circuit with linear threshold gates, which are stronger than majority gates). Our second main result is that even a modest improvement of our quantified derandomization algorithm would yield a non-trivial algorithm for standard derandomization of all of $TC^0$, and would consequently imply that $NEXP\not\subseteq TC^0$. Specifically, if there exists a quantified derandomization algorithm that gets as input a $TC^0$ circuit with depth $d$ and $n^{1+O(1/d)}$ wires (rather than $n^{1+\exp(-d)}$ wires), runs in time at most $2^{n^{\exp(-d)}}$, and distinguishes between the case that $C$ rejects at most $2^{n^{1-1/5d}}$ inputs and the case that $C$ accepts at most $2^{n^{1-1/5d}}$ inputs, then there exists an algorithm with running time $2^{n^{1-\Omega(1)}}$ for standard derandomization of $TC^0$.Comment: Changes in this revision: An additional result (a PRG for quantified derandomization of depth-2 LTF circuits); rewrite of some of the exposition; minor correction

Structure-Based Model of RNA Pseudoknot Captures Magnesium-Dependent Folding Thermodynamics

We develop a simple, coarse-grained approach for simulating the folding of the Beet Western Yellow Virus (BWYV) pseudoknot toward the goal of creating a transferable model that can be used to study other small RNA molecules. This approach combines a structure-based model (SBM) of RNA with an electrostatic scheme that has previously been shown to correctly reproduce ionic condensation in the native basin. Mg2+ ions are represented explicitly, directly incorporating ion-ion correlations into the system, and K+ is represented implicitly, through the mean-field generalized Manning counterion condensation theory. Combining the electrostatic scheme with a SBM enables the electrostatic scheme to be tested beyond the native basin. We calibrate the SBM to reproduce experimental BWYV unfolding data by eliminating overstabilizing backbone interactions from the molecular contact map and by strengthening base pairing and stacking contacts relative to other native contacts, consistent with the experimental observation that relative helical stabilities are central determinants of the RNA unfolding sequence. We find that this approach quantitatively captures the Mg2+ dependence of the folding temperature and generates intermediate states that better approximate those revealed by experiment. Finally, we examine how our model captures Mg2+ condensation about the BWYV pseudoknot and a U-tail variant, for which the nine 3' end nucleotides are replaced with uracils, and find our results to be consistent with experimental condensation measurements. This approach can be easily transferred to other RNA molecules by eliminating and strengthening the same classes of contacts in the SBM and including generalized Manning counterion condensation

Diagonal quantum Bianchi type IX models in N=1 supergravity

We take the general quantum constraints of N=1 supergravity in the special case of a Bianchi metric, with gravitino fields constant in the invariant basis. We construct the most general possible wave function which solves the Lorentz constraints and study the supersymmetry constraints in the Bianchi Class A Models. For the Bianchi-IX cases, both the Hartle-Hawking state and wormhole state are found to exist in the middle fermion levels.Comment: plain LaTex, 17 pages, accepted for publication in Classical Quantum Gravit

Cryptosporidium in fish: alternative sequencing approaches and analyses at multiple loci to resolve mixed infections

Currently, the systematics, biology and epidemiology of piscine Cryptosporidium species are poorly understood. Here, we compared Sanger ‒ and next-generation ‒ sequencing (NGS), of piscine Cryptosporidium, at the 18S rRNA and actin genes. The hosts comprised 11 ornamental fish species, spanning four orders and eight families. The objectives were: to (i) confirm the rich genetic diversity of the parasite and the high frequency of mixed infections; and (ii) explore the potential of NGS in the presence of complex genetic mixtures. By Sanger sequencing, four main genotypes were obtained at the actin locus, while for the 18S locus, seven genotypes were identified. At both loci, NGS revealed frequent mixed infections, consisting of one highly dominant variant plus substantially rarer genotypes. Both sequencing methods detected novel Cryptosporidium genotypes at both loci, including a novel and highly abundant actin genotype that was identified by both Sanger sequencing and NGS. Importantly, this genotype accounted for 68·9% of all NGS reads from all samples (249 585/362 372). The present study confirms that aquarium fish can harbour a large and unexplored Cryptosporidium genetic diversity. Although commonly used in molecular parasitology studies, nested PCR prevents quantitative comparisons and thwarts the advantages of NGS, when this latter approach is used to investigate multiple infections

Structural Color 3D Printing By Shrinking Photonic Crystals

The rings, spots and stripes found on some butterflies, Pachyrhynchus weevils, and many chameleons are notable examples of natural organisms employing photonic crystals to produce colorful patterns. Despite advances in nanotechnology, we still lack the ability to print arbitrary colors and shapes in all three dimensions at this microscopic length scale. Commercial nanoscale 3D printers based on two-photon polymerization are incapable of patterning photonic crystal structures with the requisite ~300 nm lattice constant to achieve photonic stopbands/ bandgaps in the visible spectrum and generate colors. Here, we introduce a means to produce 3D-printed photonic crystals with a 5x reduction in lattice constants (periodicity as small as 280 nm), achieving sub-100-nm features with a full range of colors. The reliability of this process enables us to engineer the bandstructures of woodpile photonic crystals that match experiments, showing that observed colors can be attributed to either slow light modes or stopbands. With these lattice structures as 3D color volumetric elements (voxels), we printed 3D microscopic scale objects, including the first multi-color microscopic model of the Eiffel Tower measuring only 39-microns tall with a color pixel size of 1.45 microns. The technology to print 3D structures in color at the microscopic scale promises the direct patterning and integration of spectrally selective devices, such as photonic crystal-based color filters, onto free-form optical elements and curved surfaces

Depression and anxiety screening identifies patients that may benefit from treatment regardless of existing diagnoses

BACKGROUND: This study investigated the utility of depression and anxiety symptom screening in patients scheduled for total knee arthroplasty to examine differences in active symptoms according to patients\u27 mental health diagnoses and associated prescription medications. MATERIAL AND METHODS: This cross-sectional study analyzed 594 patients scheduled for total knee arthroplasty at a tertiary practice between June 2018 and December 2018. Patients completed Patient-Reported Outcomes Measurements Information System (PROMIS) Depression and Anxiety Computerized Adaptive Tests in clinic quantifying active symptoms. Mental health diagnoses and associated medications were extracted from health records. Statistical analysis assessed between-group differences in mean PROMIS scores and the prevalence of heightened depressive and anxiety symptoms. RESULTS: Multivariable linear regression modeling demonstrated that being diagnosed with depression without medication (β 7.1; CONCLUSION: One in seven arthroplasty patients screened reported heightened depressive and/or anxiety symptoms. Despite the majority of arthroplasty patients on antidepressants and anxiolytics having symptoms controlled, these patients remain at increased risk of heightened active symptoms

Dorsal Raphe Dopamine Neurons Modulate Arousal and Promote Wakefulness by Salient Stimuli

Ventral midbrain dopamine (DA) is unambiguously involved in motivation and behavioral arousal, yet the contributions of other DA populations to these processes are poorly understood. Here, we demonstrate that the dorsal raphe nucleus DA neurons are critical modulators of behavioral arousal and sleep-wake patterning. Using simultaneous fiber photometry and polysomnography, we observed time-delineated dorsal raphe nucleus dopaminergic (DRNDA) activity upon exposure to arousal-evoking salient cues, irrespective of their hedonic valence. We also observed broader fluctuations of DRNDA activity across sleep-wake cycles with highest activity during wakefulness. Both endogenous DRNDA activity and optogenetically driven DRNDA activity were associated with waking from sleep, with DA signal strength predictive of wake duration. Conversely, chemogenetic inhibition opposed wakefulness and promoted NREM sleep, even in the face of salient stimuli. Therefore, the DRNDA population is a critical contributor to wake-promoting pathways and is capable of modulating sleep-wake states according to the outside environment, wherein the perception of salient stimuli prompts vigilance and arousal

Quantization of the Bianchi type-IX model in supergravity with a cosmological constant

Diagonal Bianchi type-IX models are studied in the quantum theory of $N = 1$ supergravity with a cosmological constant. It is shown, by imposing the supersymmetry and Lorentz quantum constraints, that there are no physical quantum states in this model. The $k = + 1$ Friedmann model in supergravity with cosmological constant does admit quantum states. However, the Bianchi type-IX model provides a better guide to the behaviour of a generic state, since more gravitino modes are available to be excited. These results indicate that there may be no physical quantum states in the full theory of $N = 1$ supergravity with a non-zero cosmological constant. are available to be excited. These results indicate that there may be no physical quantum states in the full theory of $N = 1$ supergravity with a non-zero cosmological constant.Comment: 17 pages report DAMTP R93/3

Immunostimulatory Membrane Proteins Potentiate \u3cem\u3eH. pylori-\u3c/em\u3eInduced Carcinogenesis by Enabling CagA Translocation

Infection with Helicobacter pylori is the single greatest risk factor for developing gastric adenocarcinoma. In prospective, population-based studies, seropositivity to the uncharacterized H. pylori proteins Hp0305 and Hp1564 was significantly associated with cancer risk in East Asia. However, the mechanism underlying this observation has not been elucidated. Here, we show that Hp0305 and Hp1564 act in concert with previously ascribed H. pylori virulence mechanisms to orchestrate cellular alterations that promote gastric carcinogenesis. In samples from 546 patients exhibiting premalignant gastric lesions, seropositivity to Hp0305 and Hp1564 was significantly associated with increased gastric atrophy across all stomach conditions. In vitro, depletion of Hp0305 and Hp1564 significantly reduced levels of gastric cell-associated bacteria and markedly impaired the ability of H. pylori to stimulate pro-inflammatory cytokine production. Remarkably, our studies revealed that Hp1564 is required for translocation of the oncoprotein CagA into gastric epithelial cells. Our data provide experimental insight into the molecular mechanisms governing novel H. pylori pathogenicity factors that are strongly associated with gastric disease and highlight the potential of Hp0305 and Hp1564 as robust molecular tools that can improve identification of individuals that are highly susceptible to gastric cancer. We demonstrate that Hp0305 and Hp1564 augment H. pylori-mediated inflammation and gastric cancer risk by promoting key bacteria-gastric cell interactions that facilitate delivery of oncogenic microbial cargo to target cells. Thus, therapeutically targeting microbial interactions driven by Hp0305/Hp1564 may enable focused H. pylori eradication strategies to prevent development of gastric malignancies in high-risk populations