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1. A stability inequality for planar lens partition

   https://doi.org/10.1017/prm.2025.2  

   Bonacini, Marco; Cristoferi, Riccardo; Topaloglu, Ihsan (January 2025, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)

   Recently it has been shown that the unique local perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens, hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem. 

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2. Building a Micro/Nanotechnology Cleanroom Training

   Kuhn, Jens-Uwe; John, Demis (April 2024, Journal of advanced technological education)

   The Central Coast Partnership for Regional Industry-Focused Micro/Nanotechnology Education (CC-PRIME) is a regional collaboration between Santa Barbara City College (SBCC), the University of California Santa Barbara (UCSB), and local industry partners, with the goal of addressing a demonstrated local workforce need in the field. Existing training available through the Support Center for Microsystems Education (SCME) was adapted with input from local industry to develop an initial cleanroom training in Micro/Nanotechnology for community college students and faculty. Two summer training sessions have been implemented, with student focus groups and industry feedback guiding modifications and additional training development. Ongoing input from local industry partners and an opportunity to leverage the existing SCME curriculum that project staff and faculty were trained on have proven critical in the development of the training. Access to local cleanroom facilities and staff and initial training for community college faculty were essential to successfully implementing the project. Additional modules and trainings are being developed to build out further and broaden this initial cleanroom training. 

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3. Determining a local Hamiltonian from a single eigenstate

   https://doi.org/10.22331/q-2019-07-08-159  

   Qi, Xiao-Liang; Ranard, Daniel (July 2019, Quantum)

   null (Ed.)

   We ask whether the knowledge of a single eigenstate of a local Hamiltonian is sufficient to uniquely determine the Hamiltonian. We present evidence that the answer is ``yes" for generic local Hamiltonians, given either the ground state or an excited eigenstate. In fact, knowing only the two-point equal-time correlation functions of local observables with respect to the eigenstate should generically be sufficient to exactly recover the Hamiltonian for finite-size systems, with numerical algorithms that run in a time that is polynomial in the system size. We also investigate the large-system limit, the sensitivity of the reconstruction to error, and the case when correlation functions are only known for observables on a fixed sub-region. Numerical demonstrations support the results for finite one-dimensional spin chains (though caution must be taken when extrapolating to infinite-size systems in higher dimensions). For the purpose of our analysis, we define the `` k -correlation spectrum" of a state, which reveals properties of local correlations in the state and may be of independent interest. 

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4. Thermoelectric current in a graphene Cooper pair splitter

   https://doi.org/10.1038/s41467-020-20476-7  

   Tan, Z. B.; Laitinen, A.; Kirsanov, N. S.; Galda, A.; Vinokur, V. M.; Haque, M.; Savin, A.; Golubev, D. S.; Lesovik, G. B.; Hakonen, P. J. (December 2021, Nature Communications)

   null (Ed.)

   Abstract Generation of electric voltage in a conductor by applying a temperature gradient is a fundamental phenomenon called the Seebeck effect. This effect and its inverse is widely exploited in diverse applications ranging from thermoelectric power generators to temperature sensing. Recently, a possibility of thermoelectricity arising from the interplay of the non-local Cooper pair splitting and the elastic co-tunneling in the hybrid normal metal-superconductor-normal metal structures was predicted. Here, we report the observation of the non-local Seebeck effect in a graphene-based Cooper pair splitting device comprising two quantum dots connected to an aluminum superconductor and present a theoretical description of this phenomenon. The observed non-local Seebeck effect offers an efficient tool for producing entangled electrons. 

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5. A Review of Local Outlier Factor Algorithms for Outlier Detection in Big Data Streams

   https://doi.org/10.3390/bdcc5010001  

   Alghushairy, Omar; Alsini, Raed; Soule, Terence; Ma, Xiaogang (March 2021, Big Data and Cognitive Computing)

   null (Ed.)

   Outlier detection is a statistical procedure that aims to find suspicious events or items that are different from the normal form of a dataset. It has drawn considerable interest in the field of data mining and machine learning. Outlier detection is important in many applications, including fraud detection in credit card transactions and network intrusion detection. There are two general types of outlier detection: global and local. Global outliers fall outside the normal range for an entire dataset, whereas local outliers may fall within the normal range for the entire dataset, but outside the normal range for the surrounding data points. This paper addresses local outlier detection. The best-known technique for local outlier detection is the Local Outlier Factor (LOF), a density-based technique. There are many LOF algorithms for a static data environment; however, these algorithms cannot be applied directly to data streams, which are an important type of big data. In general, local outlier detection algorithms for data streams are still deficient and better algorithms need to be developed that can effectively analyze the high velocity of data streams to detect local outliers. This paper presents a literature review of local outlier detection algorithms in static and stream environments, with an emphasis on LOF algorithms. It collects and categorizes existing local outlier detection algorithms and analyzes their characteristics. Furthermore, the paper discusses the advantages and limitations of those algorithms and proposes several promising directions for developing improved local outlier detection methods for data streams. 

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