Fine-Grained Completeness for Optimization in P

We initiate the study of fine-grained completeness theorems for exact and approximate optimization in the polynomial-time regime. Inspired by the first completeness results for decision problems in P (Gao, Impagliazzo, Kolokolova, Williams, TALG 2019) as well as the classic class MaxSNP and MaxSNP-completeness for NP optimization problems (Papadimitriou, Yannakakis, JCSS 1991), we define polynomial-time analogues MaxSP and MinSP, which contain a number of natural optimization problems in P, including Maximum Inner Product, general forms of nearest neighbor search and optimization variants of the $k$-XOR problem. Specifically, we define MaxSP as the class of problems definable as $\max_{x_1,\dots,x_k} \#\{ (y_1,\dots,y_\ell) : \phi(x_1,\dots,x_k, y_1,\dots,y_\ell) \}$, where $\phi$ is a quantifier-free first-order property over a given relational structure (with MinSP defined analogously). On $m$-sized structures, we can solve each such problem in time $O(m^{k+\ell-1})$. Our results are: - We determine (a sparse variant of) the Maximum/Minimum Inner Product problem as complete under *deterministic* fine-grained reductions: A strongly subquadratic algorithm for Maximum/Minimum Inner Product would beat the baseline running time of $O(m^{k+\ell-1})$ for *all* problems in MaxSP/MinSP by a polynomial factor. - This completeness transfers to approximation: Maximum/Minimum Inner Product is also complete in the sense that a strongly subquadratic $c$-approximation would give a $(c+\varepsilon)$-approximation for all MaxSP/MinSP problems in time $O(m^{k+\ell-1-\delta})$, where $\varepsilon > 0$ can be chosen arbitrarily small. Combining our completeness with~(Chen, Williams, SODA 2019), we obtain the perhaps surprising consequence that refuting the OV Hypothesis is *equivalent* to giving a $O(1)$-approximation for all MinSP problems in faster-than-$O(m^{k+\ell-1})$ time

Outcomes of Endolymphatic Sac Surgery for Meniere’s Disease with and without Comorbid Migraine

Purpose. To explore outcomes of endolymphatic sac surgery for patients with Meniere’s disease with and without the comorbid condition of migraine. Materials and Methods. A retrospective chart review of adult patients undergoing endolymphatic sac surgery at a single tertiary care center from 1987 to 2019 was performed. All adult patients who failed medical therapy and underwent primary endolymphatic sac surgery were included. The main outcome measures were vertigo control and functional level scale (FLS) score. Patient characteristics, comorbidities, and audiometric outcomes were tracked as well. Results. Patients with Meniere’s disease and migraine had a stronger association with psychiatric comorbidities (64.29% vs. 25.80%, p = 0.01), shorter duration of vertigo episodes (143 vs. 393 min, p = 0.02), and younger age (36.6 vs. 50.8 yr, p = 0.005) at the time of endolymphatic sac surgery. Postoperative pure tone averages and word recognition scores were nearly identical to preoperative baselines. Class A vertigo control (47.92%) was most common, followed by class B vertigo control (31.25%). The FLS score improved from 4.2 to 2.8 (p \u3c 0.001). Both patients with and without migraine had classes A-B vertigo control (66.67% vs. 80.95%) without any statistically significant difference (p = 0.59). Of the patients who required secondary treatment (10.42%), none had migraine. Conclusions. Endolymphatic sac surgery is an effective surgical intervention for Meniere’s disease with and without migraine. Patients with comorbid migraine tend to be younger and present with psychiatric comorbidities

Obesity Reduces Left Ventricular Strains, Torsion, and Synchrony in Mouse Models: A Cine Displacement Encoding with Stimulated Echoes (DENSE) Cardiovascular Magnetic Resonance Study

BACKGROUND: Obesity affects a third of adults in the US and results in an increased risk of cardiovascular mortality. While the mechanisms underlying this increased risk are not well understood, animal models of obesity have shown direct effects on the heart such as steatosis and fibrosis, which may affect cardiac function. However, the effect of obesity on cardiac function in animal models is not well-defined. We hypothesized that diet-induced obesity in mice reduces strain, torsion, and synchrony in the left ventricle (LV). METHODS: Ten 12-week-old C57BL/6 J mice were randomized to a high-fat or low-fat diet. After 5 months on the diet, mice were imaged with a 7 T ClinScan using a cine DENSE protocol. Three short-axis and two long-axis slices were acquired for quantification of strains, torsion and synchrony in the left ventricle. RESULTS: Left ventricular mass was increased by 15% (p = 0.032) with no change in volumes or ejection fraction. Subepicardial strain was lower in the obese mice with a 40% reduction in circumferential strain (p = 0.008) a 53% reduction in radial strain (p = 0.032) and a trend towards a 19% reduction in longitudinal strain (p = 0.056). By contrast, subendocardial strain was modestly reduced in the obese mice in the circumferential direction by 12% (p = 0.028), and no different in the radial (p = 0.690) or longitudinal (p = 0.602) directions. Peak torsion was reduced by 34% (p = 0.028). Synchrony of contraction was also reduced (p = 0.032) with a time delay in the septal-to-lateral direction. CONCLUSIONS: Diet-induced obesity reduces left ventricular strains and torsion in mice. Reductions in cardiac strain are mostly limited to the subepicardium, with relative preservation of function in the subendocardium. Diet-induced obesity also leads to reduced synchrony of contraction and hypertrophy in mouse models

Regional patterns of transition at Çadir Höyük in the Byzantine period

Byzantine archaeological sites tend to be seen as representative of the empire as a whole, with little concern given to regional context. Within the imperial narrative that shapes Byzantine history, sites—whether urban or rural—are often used to explain and illustrate imperial trends. However, when we remove that overarching narrative, the sites in Anatolia provide the potential to view them as singular examples of local and regional identity. In this article, we have separated out four types of data: fortifications, coins, faunal material, and archaeobotanical evidence to illustrate how a close examination of the data provides new ways of understanding regional identity. In doing so, we posit that the Byzantine empire needs to be seen as a collection of local identities working alongside one another, but always expressing individual needs and resources

Not the End of the World? Post-Classical Decline and Recovery in Rural Anatolia

Between the foundation of Constantinople as capital of the eastern half of the Roman Empire in 330 CE and its sack by the Fourth Crusade in 1204 CE, the Byzantine Empire underwent a full cycle from political-economic stability, through rural insecurity and agrarian decline, and back to renewed prosperity. These stages plausibly correspond to the phases of over-extension (K), subsequent release (Ω) and recovery (α) of the Adaptive Cycle in Socio-Ecological Systems. Here we track and partly quantify the consequences of those changes in different regions of Anatolia, firstly for rural settlement (via regional archaeological surveys) and secondly for land cover (via pollen analysis). We also examine the impact of climate changes on the agrarian system. While individual histories vary, the archaeological record shows a major demographic decline between ca .650 and ca. 900 CE in central and southwestern Anatolia, which was then a frontier zone between Byzantine and Arab armies. In these regions, and also in northwest Anatolia, century-scale trends in pollen indicate a substantial decline in the production of cereal and tree crops, and a smaller decline in pastoral activity. During the subsequent recovery (α) phase after 900 CE there was strong regional differentiation, with central Anatolia moving to a new economic system based on agro-pastoralism, while lowland areas of northern and western Anatolia returned to the cultivation of commercial crops such as olive trees. The extent of recovery in the agrarian economy was broadly predictable by the magnitude of its preceding decline, but the trajectories of recovery varied between different regions

Spectral Analyses of Gully-Associated Light-Toned Materials from TGO/CaSSIS and MRO/HiRISE Observations: Implications for Martian Gully Formation Mechanisms

International audienc

XX Sex Chromosome Complement Promotes Atherosclerosis in Mice

Men and women differ in circulating lipids and coronary artery disease (CAD). While sex hormones such as estrogens decrease CAD risk, hormone replacement therapy increases risk. Biological sex is determined by sex hormones and chromosomes, but effects of sex chromosomes on circulating lipids and atherosclerosis are unknown. Here, we use mouse models to separate effects of sex chromosomes and hormones on atherosclerosis, circulating lipids and intestinal fat metabolism. We assess atherosclerosis in multiple models and experimental paradigms that distinguish effects of sex chromosomes, and male or female gonads. Pro-atherogenic lipids and atherosclerosis are greater in XX than XY mice, indicating a primary effect of sex chromosomes. Small intestine expression of enzymes involved in lipid absorption and chylomicron assembly are greater in XX male and female mice with higher intestinal lipids. Together, our results show that an XX sex chromosome complement promotes the bioavailability of dietary fat to accelerate atherosclerosis