Let {$\Gamma(k)$} denote {$(k-1)!$}, and let {$\Gamma_{n}(k)$} denote {$(k-1)!$}, where {$n \in \{3,\ldots,16\}$} and {$k \in \{2\} \cup [2^{\textstyle 2^{n-3}}+1,\infty) \cap \mathbb N$}. For an integer {$n \in \{3,\ldots,16\}$}, let $\Sigma_n$ denote the following statement: if a system of equations {${\mathcal S} \subseteq \{\Gamma_{n}(x_i)=x_k:~i,k \in \{1,\ldots,n\}\} \cup \{x_i \cdot x_j=x_k:~i,j,k \in \{1,\ldots,n\}\}$} with $\Gamma$ instead of $\Gamma_{n}$ has only finitely many solutions in positive integers {$x_1,\ldots,x_n$}, then every tuple {$(x_1,\ldots,x_n) \in (\mathbb N \setminus \{0\})^n$} that solves the original system ${\mathcal S}$ satisfies {$x_1,\ldots,x_n \leqslant 2^{\textstyle 2^{n-2}}$}. Our hypothesis claims that the statements {$\Sigma_{3},\ldots,\Sigma_{16}$} are true. The statement {$\Sigma_6$} proves the following implication: if the equation {$x(x+1)=y!$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(1,2),(2,3)\}$}. The statement {$\Sigma_6$} proves the following implication: if the equation {$x!+1=y^2$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(4,5),(5,11),(7,71)\}$}. The statement {$\Sigma_9$} implies the infinitude of primes of the form {$n^2+1$}. The statement {$\Sigma_9$} implies that any prime of the form {$n!+1$} with {$n \geqslant 2^{\textstyle 2^{9-3}}$} proves the infinitude of primes of the form {$n!+1$}. The statement {$\Sigma_{14}$} implies the infinitude of twin primes. The statement {$\Sigma_{16}$} implies the infinitude of Sophie Germain primes.

As a kind of converse of the celebrated Erd˝os-Szekeres theorem, we present a necessary and sufficient condition for a sequence of length n to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths x and y, respectively.

Multiple myeloma (MM) is characterized by the malignant proliferation of monoclonal plasma cells in the bone marrow with an elevation in monoclonal paraprotein, renal impairment, hypercalcemia, lytic bony lesions, and anemia. Immune cells and associated cytokines play a significant role in MM growth, progression, and dissemination. While some cytokines and their clinical significance are well described in MM biology, others remain relatively unknown. The aim of the present study was to assess the impact of pretreatment serum levels of 27 selected cytokines on progression-free survival (PFS) and overall survival (OS) in MM patients before first-line therapy with bortezomib-based regimens. Serum cytokine levels were assayed with a Bio-Rad Bio-Plex Pro Human Cytokine 27-Plex Assay on the MAGPIX Multiplex Reader and the Bio-Plex® 200 System (Bio-Rad) including IL-1β, IL-1Ra, IL-2, IL-4, IL-5, IL-6, IL-7, IL-8, IL-9, IL-10, IL-12, IL-13, IL-15, IL-17, Eotaxin, FGF, G-CSF, GM-CSF, IFN-γ, IP-10, MCP-1, MIP-1α, MIP-1β, PDGF-BB, RANTES, TNF-α, and VEGF. A total of 61 MM patients were examined. Most patients received a bortezomib, cyclophosphamide and dexamethasone (VCD) chemotherapy regimen. In the final multivariate model, IL-13 cytokine level (HR 0.1411, 95% CI: 0.0240-0.8291, p = 0.0302), and ASCT (HR 0.3722, 95% CI: 0.1826-0.7585, p=0.0065) significantly impacted PFS. Furthermore, ASCT (HR 0.142, 95% CI: 0.046-0.438, p=0.0007), presence of bone disease at diagnosis (HR 3.826, 95% CI: 1.471-9.949, p=0.0059) and two cytokine levels- IL-1Ra (HR 1.017, 95% CI: 1.004-1.030, p= 0.0091) and IL-4 (HR 0.161, 95% CI: 0.037-0.698, p = 0.0147) were independent predictors of OS. Three clusters of MM patients were identified with different cytokine profiles. In conclusion, serum pretreatment levels of IL-13 and IL-4 are predictors of better PFS and OS, respectively, whereas IL-1Ra pretreatment levels negatively impact OS in MM patients treated with bortezomib-based chemotherapy. Cytokine signature profile may have a potential influence on the outcome of patients treated with bortezomib.

The following system of equations {x_1 \cdot x_1=x_2, x_2 \cdot x_2=x_3, 2^{2^{x_1}}=x_3, x_4 \cdot x_5=x_2, x_6 \cdot x_7=x_2} has exactly one solution in ({\mathbb N}\{0,1})^7, namely (2,4,16,2,2,2,2). Hypothesis 1 states that if a system of equations S \subseteq {x_i \cdot x_j=x_k: i,j,k \in {1,...,7}} \cup {2^{2^{x_j}}=x_k: j,k \in {1,...,7}} has at most five equations and at most finitely many solutions in ({\mathbb N}\{0,1})^7, then each such solution (x_1,...,x_7) satisfies x_1,...,x_7 \leq 16. Hypothesis 1 implies that there are infinitely many composite numbers of the form 2^{2^{n}}+1. Hypotheses 2 and 3 are of similar kind. Hypothesis 2 implies that if the equation x!+1=y^2 has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(4,5),(5,11),(7,71)}. Hypothesis 3 implies that if the equation x(x+1)=y! has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(1,2),(2,3)}. We describe semi-algorithms sem_j (j=1,2,3) that never terminate. For every j \in {1,2,3}, if Hypothesis j is true, then sem_j endlessly prints consecutive positive integers starting from 1. For every j \in {1,2,3}, if Hypothesis j is false, then sem_j prints a finite number (including zero) of consecutive positive integers starting from 1.

While multiple myeloma (MM) treatment with proteasome inhibitors and other agents yields encouraging results, primary and secondary resistance remains an emerging problem. An important factor in such treatment resistance is the overexpression of several proteins. The present study comprehensively evaluates the expression of POMP, PSMB5, NRF2, XBP1, cMAF and MAFb proteins in plasma cells isolated from the bone marrow of 39 MM patients treated with bortezomib-based regimens using enzyme-linked immunosorbent assay (ELISA). The proteins were selected on the basis of previous laboratory and clinical studies in bortezomib treated MM patients. It was found that the expression of the investigated proteins did not significantly differ between bortezomib-sensitive and bortezomib-refractory patients. However, the expression of some proteins correlated with overall survival (OS); this was significantly shorter in patients with higher POMP expression (HR 2.8, 95% CI: 1.1-7.0, p = 0.0277) and longer in those with higher MAFB expression (HR 0.32, 95% CI: 0.13-0.80, p = 0.0147). Our results indicate that high expression of POMP and MAFB in MM plasma cells may serve as predictors of OS in MM patients treated with bortezomib-based regimens. However, further studies are needed to determine the role of these factors in effective strategies for improving anti-myeloma therapy.

In developing countries today, population growth and the penetration of higher standard of living appliances in homes has resulted in a rapidly increasing residential load. In South Africa, the recent rolling blackouts and electricity price increase only highlighted this reality calling for sustainable measures to reduce the overall consumption and peak load. The dawn of the smart grid concept, embedded systems and ICTs have paved the way to novel HEMS design. In this regard, the Internet of Things (IoT), an enabler for smart and efficient energy management systems is seeing increasing attention for optimizing HEMS design and mitigate its deployment cost constraints. In this work, we propose an IoT platform for residential energy management applications focusing on interoperability, low-cost, technology availability and scalability. We focus on the backend complexities of IoT Home Area Networks (HAN) using the OCF IoTivity-Lite middleware. To augment the quality, servicing and reduce cost and complexities, this work leverages open-source Cloud technologies from Back4App as BaaS to provide consumer and Utilities with a data communication platform within an experimental study illustrating time and space agnostic “mind-changing” energy feedback, Demand Response Management (DRM) and appliance operation control via a HEM App via an Android smartphone.

The Smartphone industry has expanded significantly over the last few years. According to the available data, each year, a marked increase in the number of devices in use is observed. Most consumers opt for Smartphones due to the extensive number of software applications that can be downloaded on their devices, thus increasing their functionality. However, this growing trend of application installation brings an issue of user protection, as most applications seek permission to access data on a user’s device. The risks this poses to sensitive data is real to both corporate and individual users. While Android has grown in popularity, this trend has not been followed by the efforts to increase the security of its users. This is a well-known set of problems, and prior solutions have approached it from the ground up; that is, they have focused on implementing reasonable security policies within the Android’s open-source kernel. While these solutions have achieved the goals of improving Android with such security policies, they are severely hampered by the way in which they have implemented them. In this work, a framework referred to as CenterYou is proposed to overcome these issues. It applies a pseudo data technique and a cloud-based decision-making system to scan and protect Smartphone devices from unnecessarily requested permissions by installed applications and identifies potential privacy leakages. The current paper demonstrated all aspects of the CenterYou application technical design. The work presented here provides a significant contribution to the field, as the technique based on pseudo data is used in the actual permissions administration of Android applications. Moreover, this system is user and cloud-driven, rather than being governed by over-privileged applications.

With the targets of petroleum exploration transferred to the deep and ancient strata, abundant oil and gas resources have been found in the Lower Paleozoic and older strata in central and western China. Due to complex evolutionary processes including multiple episodes of hydrocarbon accumulation and ubiquitously accompanied by secondary alterations, significant uncertainties were remained for the generation time and accumulation processes of these revealed petroleum. In this paper, relative pure Re and Os elements existing in the asphaltene fractions of Lower Cambrian solid bitumen collected from the Guangyuan area, western Sichuan Basin, SW China and another Middle–Lower Ordovician heavy oils in the Aiding area of the Tahe oilfield in the Tarim Basin, NW China were successfully obtained by the sample pre-treatments, and Re–Os isotopic analysis was subsequently carried out for the dating of these two petroleum. The Re–Os isotopic composition indicates a generation time of Guangyuan bitumen to locate between 572 Ma and 559 Ma, corresponding to the late Sinian period of Neoproterozoic era. By the means of Re–Os isochron ages, initial 187Os/188Os ratios, and carbon isotopic compositions, the Lower Cambrian bitumen is supposed to be originated from source rocks of the Doushantuo Formation in the Sinian strata and subsequently migrated into the reservoirs of Dengying Formation. These previously reserved petroleum had been transformed to present bitumen by the destruction of reservoirs caused by tectonic uplift. The Re–Os dating results of Middle–Lower Ordovician heavy oil of Tarim Basin supposed that it was formed between 450 Ma to 436 Ma, corresponding to the Late Ordovician–Early Silurian system, and the generated petroleum is likely to migrate into the Middle–Lower Ordovician karst reservoirs to form early oil reservoirs. With tectonic uplift, these oil reservoirs were degraded and reformed to be present heavy oil reservoirs.