Nonstandard Regime Research Articles

Probability of total domination for transient reflecting processes in a quadrant

AbstractWe consider two-dimensional Lévy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that the reflected process escapes to infinity along one of the axes. Under rather general conditions, it is shown that such behaviour is certain and each component can dominate the other with positive probability for any given starting position. Additionally, we establish the corresponding invariance principle providing justification for the use of the reflected Brownian motion as an approximate model. Focusing on the probability that the first component dominates, we derive a kernel equation for the respective Laplace transform in the starting position. This is done for the compound Poisson model with negative exponential jumps and, by means of approximation, for the Brownian model. Both equations are solved via boundary value problem analysis, which also yields the domination probability when starting at the origin. Finally, certain asymptotic analysis and numerical results are presented.

Abstract 422: Sequential targeted therapy and immunotherapy of a BRAF positive metastatic melanoma patient with BRAF inhibitor vemurafenib, MEK inhibitor cobimetnib and a novel PD-1 antibody Sintilimab

Abstract Targeted therapy has dramatically improved the outcome of BRAF mutated melanoma patients. However, its response is usually brisk and lacks the durability of immunotherapy. Decisions about targeted therapy alone, immunotherapy alone, targeted therapy/immunotherapy combination or immunotherapy after targeted therapy require an oncologist to comprehensively evaluate multiple clinical factors. Here we report the sequential treatment of a BRAF positive metastatic melanoma patient with non-standard regimes due to practical reasons. A 75-year old male patient presented a black cauliflower-like mass on back and bilateral axillary lymph nodes enlargement. Postoperative pathologic examination confirmed a nodular malignant melanoma of 1.6 cm in diameter and 0.7 cm thick. NGS sequencing of the tumor revealed the canonical BRAF V600E mutation. As vemurafenib was the only approved melanoma targeted therapy drug in China at the time of diagnosis, it was administered (960 mg bid) as first-line therapy since September 2019 and the patient's response was confirmed by the significant reduction and softening of the left axillary node. One month later the node rapidly enlarged to 15 cm, and the blood scab fell off followed by pulsatile massive hemorrhage (~1000 mL). We performed an emergent angiograph and a transarterial embolization (TAE), aimed at selectively occluding the tumor artery by using gelatin sponge particle and coils. The hemorrhage was significantly reduced after TAE therapy and a left axillary residual cavity was formed. When the patient presented a progression of lymph node metastases, BRAF/MEK inhibitor combination was selected as the second-line therapy from December 2019. He received vemurafenib at a dose of 480 mg bid combined with cobimetinib 60mg qd (3 consecutive weeks every 28 days), the treatment was ongoing till disease progression in April 2020. Immunohistochemical analysis of the biopsy specimen demonstrated PD-L1 expression in 4% of tumor cells and immunotherapy was chosen as the third-line therapy. Sintilimab, a PD-1 antibody approved in China for the treatment of classical Hodgkin lymphoma, is undergoing clincial trials for multiple solid tumors including melanoma. Given the high cost of immunotherapy and the fact that Sintilimab is the only PD-1 inhibitor included in China's National Reimbursement Drug List, the patient started off-label use of Sintilimab and achieved partial response. In summary, our patient had an unconventional timeline of multiple therapies including surgery, TAE, targeted therapy and immunotherapy. His case demonstrated that meaningful clinical responses can be achieved with sequential targeted therapy/immunotherapy in BRAF-mutated metastatic melanoma and the novel PD-1 antibody Sintilimab is worth further investigation for its efficacy in metastatic melanoma. Citation Format: Yu Zhang, Xiaomo Li, Tonghui Ma, Baoshan Cao. Sequential targeted therapy and immunotherapy of a BRAF positive metastatic melanoma patient with BRAF inhibitor vemurafenib, MEK inhibitor cobimetnib and a novel PD-1 antibody Sintilimab [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr 422.

Disparity in Performance of the Czech Construction Sector: Evidence from the Markov-Switching Model

Activities in the construction sector are assumed to be influenced by inflow of mortgage funding in the private housing sector and public finances targeted at large infrastructure projects, apart from climate variables. In this study, we modeled seasonal time series representing monthly output in the Czech construction sector in CZK mil. during 2000:1 through 2016 : 12 (T = 204) adjusted for calendar variations and seasonal movements via TRAMO‑SEATS and then transformed to natural logarithms of gross returns. A Markov‑Switching model with two states, no intercept, average monthly temperature, average monthly precipitation and parameters of first‑order autoregression process was specified and estimated by the Expectation‑Maximization. In State 1 of regular performance, the log‑differenced returns were significantly and positively influenced by precipitation levels, but not by ambient outdoor temperature. In State 2 of non‑standard operation of the construction sector, the transformed series was unaffected by precipitation levels, but instead by ambient outdoor temperatures. First‑order autocorrelation dependency in both regimes was established. Changes in legal and macroeconomic environment pertinent to tax law amendments affecting VAT or corporate tax, country’s accession to EU or large construction project deadlines were shown to induce nonstandard regime in the construction sector (State 2). The model classified 91 % observations in the first state, while only 9 % data belonged to the State 2. Transition probability matrix indicates that change from model State 1 to State 2 is difficult to attain. At the same time, once State 2 was established, it tends to persist or change to State 1 with near equal probability. Ability of the Markov‑Switching model to identify both states is reasonably good.

Farey sequence in the appearance of subharmonic Shapiro steps.

The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence. In the standard regime, the appearance of half-integer and other subharmonic steps between the large harmonic steps, and their relative sizes follow the Farey construction. In the nonstandard regime, however, the half-integer steps are larger than harmonic ones, and Farey construction is only present in the appearance of higher order subharmonic steps. The examination of Lyapunov exponents has also shown that regardless of the substrate potential or deformation, there was no chaos in the system.

Model of the Optical Emission of a Driven Semiconductor Quantum Dot: Phonon-Enhanced Coherent Scattering and Off-Resonant Sideband Narrowing

We study the crucial role played by the solid-state environment in determining the photon emission characteristics of a driven quantum dot. For resonant driving, we predict a phonon enhancement of the coherently emitted radiation field with increasing driving strength, in stark contrast to the conventional expectation of a rapidly decreasing fraction of coherent emission with stronger driving. This surprising behavior results from thermalization of the dot with respect to the phonon bath and leads to a nonstandard regime of resonance fluorescence in which significant coherent scattering and the Mollow triplet coexist. Off resonance, we show that despite the phonon influence, narrowing of dot spectral sideband widths can occur in certain regimes, consistent with an experimental trend.

Field-effect transistor with a prismoidal controlling gate

A very short-channel field-effect transistor (FET), which is controlled by a nonplanar prismoidal gate, is proposed and its stationary JV characteristics are derived. The prismoidal gate effectively depletes a thin electron channel in a very narrow strip around the gate apex. Interaction of the channel electrons with a controlling gate potential is additionally focused by a selected two-layer dielectric separating the channel and gate. It is shown that in the considered FETs there exist both “standard” regimes characterized by quasisaturation of the drain current jD, with an increase in the drain-source voltage uDS, and nonstandard regimes, with drooping jDuDS characteristics and a “self-blocking” current jD. We consider the dependence of the channel conductance on the gate curvature near the apex.

Birth and Morphological Evolution of Step Bunches under Electromigration

We analyze the dynamics of electromigration-induced step bunching in the absence of desorption. We show that, even when the instability occurs at long wavelength, hinting to a smooth morphology, the surface suddenly splits into bunches escorted with wide terraces, in agreement with several observations. As the size of the bunches increases, a nonstandard regime is exhibited, namely, the bunches do not match tangentially to the facet, as would the classical Pokrosvky-Talapov shape dictate. This Letter presents a complete scenario of evolution of bunches from their birth up to their ultimate stage.

A nonstandard higher order FDTD algorithm for 3-D arbitrarily and fractal-shaped antenna structures on general curvilinear lattices

A new higher order finite-difference time-domain (FDTD) methodology for the consistent modeling of arbitrarily shaped antennas in three-dimensional (3D) curvilinear coordinates is presented in this paper. The generalized algorithm, which introduces novel conventional and nonstandard regimes, develops advanced PMLs and compact differences to handle the widened spatial increments. Also, a systematic leapfrog integrator with mesh expansion concepts is established. Beyond diverse 3D structures, analysis studies fractal arrays whose self-similarity renders them ideal for small-sized designs. Results indicate that the proposed method achieves a critical elimination of lattice errors and provides very precise radiation patterns.

Effects of heavy metal ions on intercellular communication in syriam hamster embryo cells

Several heavy metal salts [NiSO4, Cd(CH3COO)2, Pb(CH3COO)2, K2CrO4, CrCl3] were examined for their effects on intercellular communication in primary Syrian hamster embryo (SHE) cells and in the 12-O-tetradecanoyl-phorbol-13-acetate (TPA)-sensitive SHE cell line BPNi. Two exposure regimes were used: the standard regime where the exposure occurred after the cells had grown to confluence; and a non-standard regime where a high number of cells were seeded in a medium containing the metal salts. None of the chemicals were potent inhibitors of communication, i.e. effects were only found at concentrations that were non-compatible with long-term survival of the cells. NiSO4 inhibited communication in both regimes and in both cell types, but the effect was more pronounced for BPNi cells in the non-standard regime. K2CrO4 inhibited communication in the non-standard regime in both cell types, but significantly increased communication in the standard regime in BPNi cells. Similar effects were not found with CrCl3 or KCl. Thus, they were due to the properties of the CrO4(2-) ion. K2CrO4 upregulated communication in TPA-exposed BPNi cells. A high concentration of SO4(2-) did not influence the K2CrO4 inhibition in the non-standard regime, but it significantly inhibited the K2CrO4-induced increase in communication in the standard regime in BPNi cells. This suggests that K2CrO4 acts through two different mechanisms in the two exposure regimes. The CrO4(2-)-sensitive site that causes enhancement of communication in the standard regime is probably intracellular, while the site causing CrO4(2-) inhibition in the formation of gap junctional communication in the non-standard regime is most likely to be extracellular.