On the structure and the joint spectrum of a pair of commuting isometries

The study of a pair $(V_1,V_2)$ of commuting isometries is a classical theme. We shine new light on it by using the defect operator. In the cases when the defect operator is zero or positive or negative, or the difference of two mutually orthogonal projections with ranges adding up to $\ker (V_1V_2)^*$, we write down structure theorems for $(V_1,V_2)$. The structure theorems allow us to compute the joint spectrum in each of the cases above. Moreover, in each case, we also point out at which stage of the Koszul complex the exactness breaks. A pair of operator valued functions $(\varphi_1,\varphi_2)$ is canonically associated by Berger, Coburn and Lebow with $(V_1,V_2)$. If $(V_1,V_2)$ is a pure pair, then in each case above we show that \sigma(V_1,V_2)=\overline{\cup_{z\in\D} \sigma(\varphi_1(z),\varphi_2(z))}. It has been known that the fundamental pair of commuting isometries with positive defect is the pair of multiplication operators by the coordinate functions on the Hardy space of the bidisc. A major contribution of this note is to figure out the fundamental pair of commuting isometries with negative defect. This pair of commuting isometries is constructed on the Hardy space of the bidisc.Comment: 29 page

On factorization of the shift semigroup

Let $\mathscr{S}^\mathcal{E}=(S_t^\mathcal{E})_{t\ge 0}$ on $L^2(\mathbb{R}_+,\mathcal{E})$ be the right shift semigroup for a separable Hilbert space $\mathcal{E}$. Let $\mathscr{V}_1 = (V_{1,t})_{t\ge 0}$ and $\mathscr{V}_2 = (V_{2,t})_{t\ge 0}$ be a pair of semigroups of contractions which satisfy $V_{1,t}V_{2,s} = V_{2,s}V_{1,t}$ and $S^\mathcal{E}_t=V_{1,t} V_{2,t}$ for every $s,t \ge 0$. Such a pair is called a factorization of $\mathscr{S}^\mathcal{E}$. The main result of this note completely describes all factorizations of $\mathscr{S}^\mathcal{E}$ when $\mathcal{E}$ is finite dimensional. Using the known fact that $\mathscr{S}^\mathcal{E}$ is unitarily equivalent to a semigroup of multiplication operators on the vector valued Hardy space $H^2_\mathbb{D}(\mathcal{E})$, we employ novel function theoretic methods and classical convex analysis to arrive at the factorization

Smart Assistive Shoes for the Blind People

This paper presents an idea about dealing with the problems faced by blind people through smart shoes and cane. Most of the people not only in India but internationally too is dealing with this issue that is blindness. Because of this inability blind people are dependent on others for their motion and other activities.We are introducing a combination of shoes and cane which will assist them in their motion and other needed activities. The shoes and cane will be detecting nearby obstacles and eventually will send a message to the receiver connected at the cane which is next given to the person holding it. So thereby, the blind person will get to know about the obstacles around them without any help or guidance of someone else. This will make them more independent

Implementation of a Speech Recognition Algorithm to Facilitate Verbal Commands for Visual Analytics Law Enforcement Toolkit

The VALET (Visual Analytics Law Enforcement Toolkit) system allows the user to visualize and predict crime hotspots and analyze crime data. Police officers have difficulty in using VALET in a mobile situation, since the system allows only conventional input interfaces (keyboard and mouse). This research focuses on introducing a new input interface to VALET in the form of speech recognition, which allows the user to interact with the software without losing functionality. First an Application Program Interface (API) that was compatible with the VALET system was found and initial code scripts to test its functionality were written. Next, the code scripts were integrated with the VALET and additional code was written to execute the commands given by the user. Lastly, more functionality was added by including a button and keywords to toggle speech recognition on/off, and a panel to display visual feedback to the user. The results from the research showed that it was easier to give simple commands by voice rather than typing them out. It helped the user with having a new way to interact with the system that was accurate but also convenient when on the move. The speech recognition was able to recognize the correct commands with a high rate of success. The implementation of the speech recognition function was able to help the police departments in interacting with the system effectively when conventional methods were not an option

Optical intra-day variability of the blazar S5 0716+714

We present an extensive recent multi-band optical photometric observations of the blazar S5 0716+714 carried out over 53 nights with two telescopes in India, two in Bulgaria, one in Serbia, and one in Egypt during 2019 November -- 2022 December. We collected 1401, 689, 14726, and 165 photometric image frames in B, V, R, and I bands, respectively. We montiored the blazar quasi-simultaneously during 3 nights in B, V, R, and I bands; 4 nights in B, V, and R; 2 nights in V, R, and I; 5 nights in B and R; and 2 nights in V and R bands. We also took 37 nights of data only in R band. Single band data are used to study intraday flux variability and two or more bands quasi-simultaneous observations allow us to search for colour variation in the source. We employ the power-enhanced F-test and the nested ANOVA test to search for genuine flux and color variations in the light curves of the blazar on intraday timescales. Out of 12, 11, 53, and 5 nights observations, intraday variations with amplitudes between ~3% and ~20% are detected in 9, 8, 31 and 3 nights in B, V, R, and I bands, respectively, corresponding to duty cycles of 75%, 73%, 58% and 60%. These duty cycles are lower than those typically measured at earlier times. On these timescales color variations with both bluer-when-brighter and redder-when-brighter are seen, though nights with no measurable colour variation are also present. We briefly discuss possible explanations for this observed intraday variability.Comment: 19 pages, 5 figures, 4 tables, Accepted for Publication in MNRA

Role of imaging in the management of thyroglossal duct cyst carcinomas (TGC-TIRADS): a single centre retrospective study over 16 years

IntroductionThyroglossal duct cyst (TGDC) is the most frequently encountered developmental anomaly in thyroid genesis with a reported incidence of 7% in the adult population. The cyst is known to develop anywhere along the pathway of thyroid descent but is more frequently seen in the infrahyoid neck in the midline. The incidence of malignancy in a TGDC is approximately 1%; a majority of these are papillary carcinomas. This study was conducted at a single tertiary care centre which spanned over a decade which adds practice changing evidence-based knowledge to existing literature on this rare entity. A comprehensive study which conclusively establishes the imaging features predictive of malignancy in TGDC carcinomas (TGDCa), the protocol for optimal management, clinical outcome and long-term survival of these patients is not available. Although TGDC carcinoma is thought to have an excellent prognosis, there is not enough data available on the long-term survival of these patients. The aim of this study was to identify whether neck ultrasound (US) can serve as an accurate imaging tool for the preoperative diagnosis of TGDC carcinomas.MethodsWe accessed the electronic medical records of 86 patients with TGDC between January 2005 to December 2021. Of these, 22 patients were detected with TGDC papillary carcinoma on histopathologic examination. Relevant imaging, treatment and follow up information for all cases of TGDC carcinoma were retrospectively reviewed. We compared US characteristics predictive of malignancy across outcomes groups; malignant vs benign using the Chi-square test. Based on the results, a TGC-TIRADS classification was proposed with calculation of the percentage likelihood of malignancy for each category.ResultsCompared to benign TGDCs, malignant TGDCs were more likely to present with following US characteristics: irregular or lobulated margins (90.40 vs. 38.10%), solid-cystic composition (61.90 vs. 17.07%), internal vascularity (47.62 vs. 4.88 %), internal calcification (76.19 vs. 7.32 %) (each p value < 0.005). Calcifications and internal vascularity were the most specific while irregular/lobulated margins were the most sensitive feature for malignancy. AUC under the ROC curve was 0.88. Allpatients were operated and were disease free at the end of 5 years or till the recent follow up.DiscussionUS is the imaging modality of choice for pre-operative diagnosis of TGDC carcinoma. Thepre-operative diagnosis and risk stratification of thyroglossal lesions will be aided by the application of the proposed TGC-TIRADS classification, for which the percentage likelihood of malignancy correlated well with the results in our study. Sistrunk procedure is adequate for isolated TGDC carcinoma; suspicious neck nodes on imaging also necessitates selective nodal dissection. Papillary carcinomas have an excellent prognosis with low incidence of disease recurrence

Search for new particles in events with energetic jets and large missing transverse momentum in proton-proton collisions at root s=13 TeV

A search is presented for new particles produced at the LHC in proton-proton collisions at root s = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb(-1), collected in 2017-2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initial-state radiation and events with large-radius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with an earlier search based on a data sample of 36 fb(-1), collected in 2016. No significant excess of events is observed with respect to the standard model background expectation determined from control samples in data. The results are interpreted in terms of limits on the branching fraction of an invisible decay of the Higgs boson, as well as constraints on simplified models of dark matter, on first-generation scalar leptoquarks decaying to quarks and neutrinos, and on models with large extra dimensions. Several of the new limits, specifically for spin-1 dark matter mediators, pseudoscalar mediators, colored mediators, and leptoquarks, are the most restrictive to date.Peer reviewe

Combined searches for the production of supersymmetric top quark partners in proton-proton collisions at root s=13 TeV

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV

Probing effective field theory operators in the associated production of top quarks with a Z boson in multilepton final states at root s=13 TeV

Peer reviewe