Thermal attenuator channels model the decoherence of quantum systems interacting with a thermal bath, e.g., a two-level system subject to thermal noise and an electromagnetic signal traveling through ...a fiber or in free-space. Hence determining the quantum capacity of these channels is an outstanding open problem for quantum computation and communication. Here we derive several upper bounds on the quantum capacity of qubit and bosonic thermal attenuators. We introduce an extended version of such channels which is degradable and hence has a single-letter quantum capacity, bounding that of the original thermal attenuators. Another bound for bosonic attenuators is given by the bottleneck inequality applied to a particular channel decomposition. With respect to previously known bounds we report better results in a broad range of attenuation and noise: we can now approximate the quantum capacity up to a negligible uncertainty for most practical applications, e.g., for low thermal noise.
We extend the concept of transfer learning, widely applied in modern machine learning algorithms, to the emerging context of hybrid neural networks composed of classical and quantum elements. We ...propose different implementations of hybrid transfer learning, but we focus mainly on the paradigm in which a pre-trained classical network is modified and augmented by a final variational quantum circuit. This approach is particularly attractive in the current era of intermediate-scale quantum technology since it allows to optimally pre-process high dimensional data (e.g., images) with any state-of-the-art classical network and to embed a select set of highly informative features into a quantum processor. We present several proof-of-concept examples of the convenient application of quantum transfer learning for image recognition and quantum state classification. We use the cross-platform software library PennyLane to experimentally test a high-resolution image classifier with two different quantum computers, respectively provided by IBM and Rigetti.
Sodium-glucose cotransporter 2 (SGLT2) inhibitors lower glycemia by enhancing urinary glucose excretion. The physiologic response to pharmacologically induced acute or chronic glycosuria has not been ...investigated in human diabetes.
We evaluated 66 patients with type 2 diabetes (62 ± 7 years, BMI = 31.6 ± 4.6 kg/m(2), HbA1c = 55 ± 8 mmol/mol, mean ± SD) at baseline, after a single dose, and following 4-week treatment with empagliflozin (25 mg). At each time point, patients received a mixed meal coupled with dual-tracer glucose administration and indirect calorimetry.
Both single-dose and chronic empagliflozin treatment caused glycosuria during fasting (median, 7.8 interquartile range {IQR}, 4.4 g/3 hours and 9.2 IQR, 5.2 g/3 hours) and after meal ingestion (median, 29.0 IQR, 12.5 g/5 hours and 28.2 IQR, 15.4 g/5 hours). After 3 hours of fasting, endogenous glucose production (EGP) was increased 25%, while glycemia was 0.9 ± 0.7 mmol/l lower (P < 0.0001 vs. baseline). After meal ingestion, glucose and insulin AUC decreased, whereas the glucagon response increased (all P < 0.001). While oral glucose appearance was unchanged, EGP was increased (median, 40 IQR, 14 g and 37 IQR, 11 g vs. 34 IQR, 11 g, both P < 0.01). Tissue glucose disposal was reduced (median, 75 IQR, 16 g and 70 IQR, 21 g vs. 93 IQR, 18 g, P < 0.0001), due to a decrease in both glucose oxidation and nonoxidative glucose disposal, with a concomitant rise in lipid oxidation after chronic administration (all P < 0.01). β Cell glucose sensitivity increased (median, 55 IQR, 35 pmol • min(-1) • m(-2) • mM(-1) and 55 IQR, 39 pmol • min(-1) • m(-2) • mM(-1) vs. 44 IQR, 32 pmol • min(-1) • m(-2) • mM(-1), P < 0.0001), and insulin sensitivity was improved. Resting energy expenditure rates and those after meal ingestion were unchanged.
In patients with type 2 diabetes, empagliflozin-induced glycosuria improved β cell function and insulin sensitivity, despite the fall in insulin secretion and tissue glucose disposal and the rise in EGP after one dose, thereby lowering fasting and postprandial glycemia. Chronic dosing shifted substrate utilization from carbohydrate to lipid. Trial registration. ClinicalTrials.Gov NCT01248364 (EudraCT no. 2010-018708-99). Funding. This study was funded by Boehringer Ingelheim.
Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of ...physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from
to
research. Model-based approaches for linking
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research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For
research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.
We consider the problem of correctly classifying a given quantum two-level system (qubit) which is known to be in one of two equally probable quantum states. We assume that this task should be ...performed by a quantum machine which does not have at its disposal a complete classical description of the two template states, but can only have partial prior information about their level of purity and mutual overlap. Moreover, similarly to the classical supervised learning paradigm, we assume that the machine can be trained by <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> qubits prepared in the first template state and by <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> more qubits prepared in the second template state. In this situation, we are interested in the optimal process which correctly classifies the input qubit with the largest probability allowed by quantum mechanics. The problem is studied in its full generality for a number of different prior information scenarios and for an arbitrary size <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> of the training data. Finite size corrections around the asymptotic limit <inline-formula> <tex-math notation="LaTeX">n\rightarrow \infty </tex-math></inline-formula> are derived. When the states are assumed to be pure, with known overlap, the problem is also solved in the case of d-level systems.
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