Non-stationary Stochastic Optimization

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We identify sharp conditions under which it is possible to achieve long-run-average optimality and more refined performance measures such as rate optimality that fully characterize the complexity of such problems. In doing so, we also establish a strong connection between two rather disparate strands of literature: adversarial online convex optimization; and the more traditional stochastic approximation paradigm (couched in a non-stationary setting). This connection is the key to deriving well performing policies in the latter, by leveraging structure of optimal policies in the former. Finally, tight bounds on the minimax regret allow us to quantify the "price of non-stationarity," which mathematically captures the added complexity embedded in a temporally changing environment versus a stationary one

An Improved Interactive Streaming Algorithm for the Distinct Elements Problem

The exact computation of the number of distinct elements (frequency moment $F_0$) is a fundamental problem in the study of data streaming algorithms. We denote the length of the stream by $n$ where each symbol is drawn from a universe of size $m$. While it is well known that the moments $F_0,F_1,F_2$ can be approximated by efficient streaming algorithms, it is easy to see that exact computation of $F_0,F_2$ requires space $\Omega(m)$. In previous work, Cormode et al. therefore considered a model where the data stream is also processed by a powerful helper, who provides an interactive proof of the result. They gave such protocols with a polylogarithmic number of rounds of communication between helper and verifier for all functions in NC. This number of rounds $\left(O(\log^2 m) \;\text{in the case of} \;F_0 \right)$ can quickly make such protocols impractical. Cormode et al. also gave a protocol with $\log m +1$ rounds for the exact computation of $F_0$ where the space complexity is $O\left(\log m \log n+\log^2 m\right)$ but the total communication $O\left(\sqrt{n}\log m\left(\log n+ \log m \right)\right)$. They managed to give $\log m$ round protocols with $\operatorname{polylog}(m,n)$ complexity for many other interesting problems including $F_2$, Inner product, and Range-sum, but computing $F_0$ exactly with polylogarithmic space and communication and $O(\log m)$ rounds remained open. In this work, we give a streaming interactive protocol with $\log m$ rounds for exact computation of $F_0$ using $O\left(\log m \left(\,\log n + \log m \log\log m\,\right)\right)$ bits of space and the communication is $O\left( \log m \left(\,\log n +\log^3 m (\log\log m)^2 \,\right)\right)$. The update time of the verifier per symbol received is $O(\log^2 m)$.Comment: Submitted to ICALP 201

Deciphering M-T diagram of shape memory Heusler alloys: reentrance, plateau and beyond

We present our recent results on temperature behaviour of magnetization observed in Ni_47Mn_39In_14 Heusler alloys. Three regions can be distinguished in the M-T diagram: (I) low temperature martensitic phase (with the Curie temperature T_CM = 140 K), (II) intermediate mixed phase (with the critical temperature T_MS = 230 K) exhibiting a reentrant like behavior (between T_CM and T_MS) and (III) high temperature austenitic phase (with the Curie temperature T_CA = 320 K) exhibiting a rather wide plateau region (between T_MS and T_CA). By arguing that powerful structural transformations, causing drastic modifications of the domain structure in alloys, would also trigger strong fluctuations of the order parameters throughout the entire M-T diagram, we were able to successfully fit all the data by incorporating Gaussian fluctuations (both above and below the above three critical temperatures) into the Ginzburg-Landau scenario

The relationship between educational level and bone mineral density in postmenopausal women

BACKGROUND: This study describes the influence of educational level on bone mineral density (BMD) and investigating the relationship between educational level and bone mineral density in postmenopausal women. METHODS: A total of 569 postmenopausal women, from 45 to 86 years of age (mean age of 60.43 ± 7.19 years) were included in this study. A standardized interview was used at the follow-up visit to obtain information on demographic, life-style, reproductive and menstrual histories such as age at menarche, age at menopause, number of pregnancies, number of abortions, duration of menopause, duration of fertility, and duration of lactation. Patients were separated into four groups according to the level of education, namely no education (Group 1 with 209 patients), elementary (Group 2 with 222 patients), high school (Group 3 with 79 patients), and university (Group 4 with 59 patients). RESULTS: The mean ages of groups were 59.75 ± 7.29, 61.42 ± 7.50, 60.23 ± 7.49, and 58.72 ± 7.46, respectively. Spine BMD was significant lower in Group 1 than that of other groups (p < 0.05). Trochanter and ward's triangle BMD were the highest in Group 4 and there was a significant difference between Group 1 and 4 (p < 0.05). The prevalence of osteoporosis showed an inverse relationship with level of education, ranging from 18.6% for the most educated to 34.4% for the no educated women (p < 0.05). Additionally, there was a significant correlation between educational level and spine BMD (r = 0.20, p < 0.01), trochanter BMD (r = 0.13, p < 0.01), and ward's BMD (r = 0.14, p < 0.01). CONCLUSIONS: The results of the study suggest that there is a significant correlation between educational level and BMD. Losses in BMD for women of lower educational level tend to be relatively high, and losses in spine and femur BMD showed a decrease with increasing educational level

Three-dimensional dualities with bosons and fermions

We propose new infinite families of non-supersymmetric IR dualities in three space-time dimensions, between Chern-Simons gauge theories (with classical gauge groups) with both scalars and fermions in the fundamental representation. In all cases we study the phase diagram as we vary two relevant couplings, finding interesting lines of phase transitions. In various cases the dualities lead to predictions about multi-critical fixed points and the emergence of IR quantum symmetries. For unitary groups we also discuss the coupling to background gauge fields and the map of simple monopole operators. \ua9 2018, The Author(s)

Proof-Carrying Data From Arithmetized Random Oracles

Proof-carrying data (PCD) is a powerful cryptographic primitive that allows mutually distrustful parties to perform distributed computation in an efficiently verifiable manner. Known constructions of PCD are obtained by recursively-composing SNARKs or related primitives. SNARKs with desirable properties such as transparent setup are constructed in the random oracle model. However, using such SNARKs to construct PCD requires heuristically instantiating the oracle and using it in a non-black-box way. Chen, Chiesa and Spooner (EC\u2722) constructed SNARKs in the low-degree random oracle model, circumventing this issue, but instantiating their model in the real world appears difficult. In this paper, we introduce a new model: the arithmetized random oracle model (AROM). We provide a plausible standard-model (software-only) instantiation of the AROM, and we construct PCD in the AROM, given only a standard-model collision-resistant hash function. Furthermore, our PCD construction is for arbitrary-depth compliance predicates. We obtain our PCD construction by showing how to construct SNARKs in the AROM for computations that query the oracle, given an accumulation scheme for oracle queries in the AROM. We then construct such an accumulation scheme for the AROM. We give an efficient lazy sampling algorithm (an emulator) for the ARO up to some error. Our emulator enables us to prove the security of cryptographic constructs in the AROM and that zkSNARKs in the ROM also satisfy zero-knowledge in the AROM. The algorithm is non-trivial, and relies on results in algebraic query complexity and the combinatorial nullstellensatz

Inhibition of focal adhesion kinase with her-2 targeted antibody pertuzumab (Omnitarg®, 2C4) in breast cancer cells

Pertuzumab (Omnitarg®, 2C4) is a recombinant humanized monoclonal antibody targeted to extracellular region of HER-2. Previous results proved the inhibitory effect of Pertuzumab on the survival of breast cancer cells via MAPK and Akt pathway. Focal adhesion kinase (FAK) regulates multiple cellular processes including growth, differentiation, adhesion, motility and apoptosis. Here, we aimed to investigate the effects of Pertuzumab on ligand activated total FAK expression and phosphorylation in the HER-2 overexpressing BT-474 breast cancer cell line. Heregulin was used for ligand activation. We have found that FAK expression and phosphorylation were inhibited in with Pertuzumab in breast cancer cells

Identification of endogenous reference genes for qRT-PCR analysis in normal matched breast tumor tissues

Quantitative gene expression measurements from tumor tissue are frequently compared with matched normal and/or adjacent tumor tissue expression for diagnostic marker gene selection as well as assessment of the degree of transcriptional deregulation in cancer. Selection of an appropriate reference gene (RG) or an RG panel, which varies depending on cancer type, molecular subtypes, and the normal tissues used for interindividual calibration, is crucial for the accurate quantification of gene expression. Several RG panels have been suggested in breast cancer for making comparisons among tumor subtypes, cell lines, and benign/malignant tumors. In this study, expression patterns of 15 widely used endogenous RGs (ACTB, TBP, GAPDH, SDHA, HPRT, HMBS, B2M, PPIA, GUSB, YWHAZ2, PGK1, RPLP0, PUM1, MRPL19, and RPL41), and three candidate genes that were selected through analysis of two independent microarray datasets (IL22RA1, TTC22, ZNF224) were determined in 23 primary breast tumors and their matched normal tissues using qRT-PCR. Additionally, 18S rRNA, ACTB, and SDHA were tested using randomly primed cDNAs from 13 breast tumor pairs to assess the rRNA/mRNA ratio. The tumors exhibited significantly lower rRNA/mRNA ratio when compared to their normals, on average. The expression of the studied RGs in breast tumors did not exhibit differences in terms of grade, ER, or PR status. The stability of RGs was examined based on two different statistical models, namely GeNorm and NormFinder. Among the 18 tested endogenous reference genes, ACTB and SDHA were identified as the most suitable reference genes for the normalization of qRT-PCR data in the analysis of normal matched tumor breast tissue pairs by both programs. In addition, the expression of the gelsolin (GSN) gene, a well-known downregulated target in breast tumors, was analyzed using the two most suitable genes and different RG combinations to validate their effectiveness as a normalization factor (NF). The GSN expression of the tumors used in this study was significantly lower than that of normals showing the effectivity of using ACTB and SDHA as suitable RGs in this set of tumor-normal tissue panel. The combinational use of the best performing two RGs (ACTB and SDHA) as a normalization factor can be recommended to minimize sample variability and to increase the accuracy and resolution of gene expression normalization in tumor-normal paired breast cancer qRT-PCR studies. Copyright © 2009 Cognizant Comm. Corp. All rights reserved