Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

A Match in Time Saves Nine: Deterministic Online Matching With Delays

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number of requests appear in a metric space at different times and the goal of an online algorithm is to match them in pairs. In contrast to traditional online matching problems, in MPMD all requests appear online and an algorithm can match any pair of requests, but such decision may be delayed (e.g., to find a better match). The cost is the sum of matching distances and the introduced delays. We present the first deterministic online algorithm for this problem. Its competitive ratio is $O(m^{\log_2 5.5})$ $= O(m^{2.46})$, where $2 m$ is the number of requests. This is polynomial in the number of metric space points if all requests are given at different points. In particular, the bound does not depend on other parameters of the metric, such as its aspect ratio. Unlike previous (randomized) solutions for the MPMD problem, our algorithm does not need to know the metric space in advance

Linear and nonlinear optical spectroscopy of a strongly-coupled microdisk-quantum dot system

A fiber taper waveguide is used to perform direct optical spectroscopy of a microdisk-quantum-dot system, exciting the system through the photonic (light) channel rather than the excitonic (matter) channel. Strong coupling, the regime of coherent quantum interactions, is demonstrated through observation of vacuum Rabi splitting in the transmitted and reflected signals from the cavity. The fiber coupling method also allows the examination of the system's steady-state nonlinear properties, where saturation of the cavity-QD response is observed for less than one intracavity photon.Comment: adjusted references, added minor clarification

Nectin-4: a new prognostic biomarker for efficient therapeutic targeting of primary and metastatic triple-negative breast cancer

International audienceBackground: Triple-negative breast cancers (TNBCs) are associated with a poor prognosis. In contrast to other molecular sub-types, they have no identified specific target and chemotherapy remains the only available systemic treatment. The adhesion molecule nectin-4 represents a new potential therapeutic target in different cancer models. Here, we have tested the prognos-tic value of nectin-4 expression and assessed the therapeutic efficiency of an anti-nectin 4 antibody drug conjugate (ADC) on localised and metastatic TNBC in vitro and in vivo. Materials and methods: We analysed nectin-4/PVRL4 mRNA expression in 5673 invasive breast cancers and searched for correlations with clinicopathological features including metastasis-free survival (MFS). Immunohistochemistry was carried out in 61 TNBCs and in samples of primary TNBC Patient-Derived Xenografts (PDXs). An anti-nectin-4 antibody eligible for ADC was produced and tested in vitro and in vivo in localised and metastatic TNBC PDXs. Results: High nectin-4/PVRL4 mRNA expression was associated with poor-prognosis features including the TN and basal sub-types. High PVRL4 mRNA expression showed independent negative prognostic value for MFS in multivariate analysis in TNBCs. Nectin-4 protein expression was not detected in adult healthy tissues including mammary tissue. Membranous protein expression was found in 62% of TNBCs, with strong correlation with mRNA expression. We developed an ADC (N41mab-vcMMAE) comprising a human anti-nectin-4 monoclonal antibody conjugated to monomethyl auristatin-E (MMAE). In vitro, this ADC bound to nectin-4 with high affinity and specificity and induced its internalisation as well as dose-dependent cytotoxicity on nectin-4-expressing breast cancer cell lines. In vivo, this ADC induced rapid, complete and durable responses on nectin-4-positive xenograft TNBC samples including primary tumours, metastatic lesions, and local relapses; efficiency was dependent on both the dose and the nectin-4 tumour expression level. Conclusion: Nectin-4 is both a new promising prognostic biomarker and specific therapeutic target for ADC in the very limited armamentarium against TNBC

Nonlinear response of the vacuum Rabi resonance

On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By employing a cavity to confine the field, the strength of this interaction can be increased many orders of magnitude to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics has been reached for real atoms in optical cavities, and for artificial atoms in circuit QED and quantum-dot systems. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity - an effect known as vacuum Rabi splitting. The circuit QED architecture is ideally suited for going beyond this linear response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet, and the appearance of additional peaks with the characteristic sqrt(n) spacing of the Jaynes-Cummings ladder. These constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.Comment: 6 pages, 4 figures. Supplementary Material and Supplementary Movies are available at http://www.eng.yale.edu/rslab/publications.htm

Reproducibility and relative validity of a semiquantitative food frequency questionnaire in European preschoolers: The ToyBox study

Objectives: The aim of this study was to examine the reproducibility and relative validity of a semiquantitative food frequency questionnaire (FFQ) in assessing food group estimates. Methods: Food group estimates were assessed via a 37-item FFQ and a 3-d food record (FR). Pearson's correlation coefficients for log-transformed values were calculated to assess the reproducibility and Spearman's rank correlation coefficients for log-transformed values were calculated to assess the validity. Kindergartens from six European countries participated in the preparatory substudies of the ToyBox intervention study; data from preschool children 4 to 6 y of age (n = 196, reproducibility study; n = 324, validation study) were obtained. Results: In the reproducibility study, positive Pearson's correlation coefficients for single and aggregated food groups ranged from 0.14 for pasta and rice to 0.90 for cooked vegetables. In the validation study, the FR gave higher estimates of 40 of the 50 food items (single and aggregated) examined compared with those obtained from the FFQ. Positive crude Spearman rank correlation coefficients ranged from 0.01 for total beverages (added sugar) and rice to 0.62 for tea. Corrections for the deattenuation effect did not improve observed correlations. Quartiles and tertiles were calculated for a small number of food groups (N = 14) owing to zero consumption in the rest of the groups. Conclusions: Moderately good reproducibility and low-moderate relative validity of the FFQ used in preschool children was observed. Relative validity, however, varied by food and beverage group; for some of the “key” foods/drinks targeted in the ToyBox intervention (e.g., biscuits), the validity was good. The findings should be considered in future epidemiologic and intervention studies in preschool children

Strong Interactions of Single Atoms and Photons near a Dielectric Boundary

Modern research in optical physics has achieved quantum control of strong interactions between a single atom and one photon within the setting of cavity quantum electrodynamics (cQED). However, to move beyond current proof-of-principle experiments involving one or two conventional optical cavities to more complex scalable systems that employ N >> 1 microscopic resonators requires the localization of individual atoms on distance scales < 100 nm from a resonator's surface. In this regime an atom can be strongly coupled to a single intracavity photon while at the same time experiencing significant radiative interactions with the dielectric boundaries of the resonator. Here, we report an initial step into this new regime of cQED by way of real-time detection and high-bandwidth feedback to select and monitor single Cesium atoms localized ~100 nm from the surface of a micro-toroidal optical resonator. We employ strong radiative interactions of atom and cavity field to probe atomic motion through the evanescent field of the resonator. Direct temporal and spectral measurements reveal both the significant role of Casimir-Polder attraction and the manifestly quantum nature of the atom-cavity dynamics. Our work sets the stage for trapping atoms near micro- and nano-scopic optical resonators for applications in quantum information science, including the creation of scalable quantum networks composed of many atom-cavity systems that coherently interact via coherent exchanges of single photons.Comment: 8 pages, 5 figures, Supplemental Information included as ancillary fil

Asexuality: Classification and characterization

This is a post-print version of the article. The official published version can be obtaineed at the link below.The term “asexual” has been defined in many different ways and asexuality has received very little research attention. In a small qualitative study (N = 4), individuals who self-identified as asexual were interviewed to help formulate hypotheses for a larger study. The second larger study was an online survey drawn from a convenience sample designed to better characterize asexuality and to test predictors of asexual identity. A convenience sample of 1,146 individuals (N = 41 self-identified asexual) completed online questionnaires assessing sexual history, sexual inhibition and excitation, sexual desire, and an open-response questionnaire concerning asexual identity. Asexuals reported significantly less desire for sex with a partner, lower sexual arousability, and lower sexual excitation but did not differ consistently from non-asexuals in their sexual inhibition scores or their desire to masturbate. Content analyses supported the idea that low sexual desire is the primary feature predicting asexual identity

Optical source of individual pairs of colour-conjugated photons

We theoretically demonstrate that Kerr nonlinearity in optical circuits can lead to both resonant four-wave mixing and photon blockade, which can be used for high-yield generation of high-fidelity individual photon pairs with conjugated frequencies. We propose an optical circuit, which, in the optimal pulsed-drive regime, would produce photon pairs at the rate up to 5 × 105  s−1 (0.5 pairs per pulse) with g(2)(0)<10–2g(2)(0)<10−2 for one of the conjugated frequencies. We show that such a scheme can be utilised to generate colour-entangled photons