Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it features regularities that can be used to determine a shortest addition chain. We show that a string with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index for N that could assemble this string. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the string so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite binary string. Once the new information is assembled by a dissipative structure or by a human, it is subject to the 2^nd law of thermodynamics, and nature seeks to optimize its assembly pathway.

For the in-house validation of a droplet digital PCR method, a factorial experimental design was implemented. This design serves different purposes. On the one hand, it is an efficient design in relation to the workload involved in achieving a desirable level of reliability of variance estimates. On the other hand, it allows a partitioning of total variance into different components, thus providing information regarding the dominant sources of random variation. The statistical modelling reflects the actual measurement mechanism, establishing relationships between nominal target DNA copies per well, the range of variation of copy numbers per droplet, probability of detection values, and estimated numbers of copies.

Multiple Gateways (GWs) provide network connectivity to Internet of Things (IoT) sensors in a Wide Area Network (WAN). The End Nodes (ENs) can connect to any GW by discovering and acquiring its periodic beacons. This provides GW diversity and hence improves coverage. If the GWs are within vicinity to each other, and they keep sending periodic beacons to be discovered, the result is interference and collisions. In this study, the impact of such intra-network interference is analyzed to determine the maximum number of GWs that can co-exist within a given urban neighborhood. The paper shows the relationship between beacon collisions and the resulting packet loss rates in a given urban environment. The expected collision rates are calculated for the Medium Access Control (MAC) layer. The eventual packet loss rates are calculated with the MAC and Physical (PHY) layers combined. For this purpose, a new co-channel interference model is presented. The model calculates the average Carrier to Interference ratio (C/I) averaged across all the colliding events. It takes into account the partial overlap durations and the relative power of each colliding signal. The model shows that a collision does not always cause a packet loss. Packet losses occur if there is a collision and if the C/I is below a threshold. The performance evaluation is presented using a combination of analytical and simulation methods. The analytical methods provide the theoretical foundation, and have been used to validate the simulation results. Furthermore, the system models are developed from experimental data obtained from measurements with real hardware. Numerical results are provided with a low bit rate Gaussian Frequency Shift Keying (GFSK) modulation at the PHY layer, which is derived from the IEEE 802.15.4 standard specification. This paper provides guidance on selecting the right GFSK modulation parameters for such low bit-rate and narrow bandwidth IoT applications. The analysis and simulation results show that larger beacon intervals help in reducing beacon loss rates, at the cost of larger beacon acquisition latency. On the flip side, the gateway discovery latency reduces with increasing GW density thanks to abundance of beacons.

Various factors, such as uncertainty of component parameters and uncertainty of sensor meas-urement values, contribute to the difficulty of fault detection in the landing gear retrac-tion/extension hydraulic system. In this paper, we introduce linear fractional transformation technology and uncertainty analysis theory for the construction of the diagnostic bond graph of the landing gear retraction/extension hydraulic system. In this way, interval analytical redundancy relations and fault signature matrix can be derived. Using the fault signature matrix, existing faults of the system can be preliminarily detected and isolated. Additionally, interval analytical re-dundancy relations can be used to detect system faults in detail, and cases analysis can be carried out to determine if the actuator is externally or internally leaky, and if the landing gear selector valve is reversing stuck. Compared to the traditional analytical redundancy relations, this method takes into account the negative factors of uncertainty; and compared to the traditional absolute diagnostic threshold, the interval diagnostic threshold is more accurate and sensitive.

We have studied the very large amount of literary works written by the Italian mystic Maria Valtorta to assess similarities and differences in her writings because she claims that most of them are due to mystical visions. We have used mathematical and statistical tools developed for specifically studying deep linguistic aspects of texts. The general trend indicates that the literary works explicitly attributable to Maria Valtorta differ significantly from her other literary works, that she claims are attributable to the alleged characters Jesus and Mary. Mathematically, they seem to have been written by different authors. The comparison with the Italian literature is very striking. A single author, namely Maria Valtorta, seems to be able to write texts so diverse to cover the entire mathematical range (suitable defined) of the Italian literature of seven centuries.

In real-life scenario, there are many mathematical tools to handle the incomplete and imprecise data. One of them is the fuzzy approach. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named as enhancing decomposition approach, is presented for achieving a subset for the parametric space that contains the sameα-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

Patients with locally advanced head and neck squamous cell carcinoma (HNSCC) frequently require primary radiochemotherapy (RCT). Despite intensity-modulation, desired radiation-induced effects observed in HNSCC, may also be observed as side-effects in healthy tissue e.g. the sternocleidomastoideus muscle (SCM). These side-effects (e.g. tissue fibrosis) depend on the interval between completion of RCT and restaging-CT. For salvage surgery, the optimal time window for surgery is currently postulated between 6 and 12 weeks after completion of RCT. Thus, no extensive tissue fibrosis is to be expected. This interval is based on studies exploring surgical complications. Studies directly exploring radiation-induced changes of the SCM in HNSCC-patients are sparse. The present study quantifies tissue alterations in SCM and paravertebral musculature (PVM) after RCT applying radiomics to determine the optimal time window for salvage surgery. Three radiomic key parameters 1) volume, 2) mean positivity of pixels (MPP) and 3) uniformity were extracted with mint lesionTM in the staging-CTs and restaging-CTs of 98 HNSCC-patients. Of these, 25 were female, the mean age was 62 (±9.6) years and 80.9% were UICC Stage IV. The mean restaging-interval was 55 (±28; range29-229) days. Only the mean volume significantly decreased after RCT from 9.0 to 8.4 and 96.5 to 91.9 ml for SCM and PVM, respectively (both p=0.007, both Cohen’s d=0.28). In addition, the mean body mass index (BMI) decreases from 23.9 (±4.2) to 21.0 (±3.6) kg/m² (p<0.001); Cohen's d = 0.9). The mean BMI-decrease significantly correlated with the volume decrease for SCM (r=0.27; p=0.007) and PVM (r=0.41; p<0.001). If t-test p-values were adjusted for the BMI-decrease, no significant change in volumes for SCM and PVM was observed (both p>0.05). The present data supports the postulated optimal interval for salvage surgery of 6 to 12 weeks. Irrespective of the remaining risk-benefit ratio of salvage surgery, the risk of additional surgical complications due to fibrosis is not supported by the present observations.

This article presents six probability distributions from the Gamma family with three parameters, for the flood frequency analysis in hydrology. The choice of the Gamma family of statistical dis-tributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the im-provement of the estimation of maximum flows and including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected pa-rameters was researched, being an element of novelty. The linear moments method is better than MOM because it avoids the choice of skewness depending on the origin of the flows, practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed, using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented like, quantile functions, the exact and ap-proximate relations for estimating parameters and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river, to verify the proposed methodology. The per-formance of this distributions is evaluated using Kiling-Gupta and Nash-Sutcliff coefficients.

This study purposes the use of plug-in electric vehicles for demand side management (DSM) considering uncertainties in demand as well as uncertainties due to mobility of PEV to mitigate peak demand. The solution also seeks to reduce electric cost in addition to reducing the effects of greenhouse gases. In recent years DSM using distributed storage system such as battery energy management system (BESS) and plugged-in electric vehicles (PEV) have become very prevalent with most implementations resorting to deterministic load forecast. These methods do not consider the potential growth in demand making their solutions less robust. In this study we propose a real-time density demand forecast and stochastic optimization for robust operation of PEV for a building. This method accounts for demand uncertainties in addition to uncertainties in mobile energy storage as found in PEV, making the resulting solution robust as compared to the deterministic case. A case study on a real site in South Korea is used for verification and testing. The proposed study is verified and tested against existing algorithms. The result verifies the effectiveness of the proposed approach

Mereotopology is a concept rooted in analytical philosophy. The phase-field concept is based on mathematical physics and finds applications in materials engineering. The two concepts seem to be disjoint at a first glance. While mereotopology qualitatively describes static relations between things like x isConnected y (topology) or x isPartOf y (mereology) by first order logic and Boolean algebra, the phase-field concept describes the geometric shape of things and its dynamic evolution by drawing on a scalar field. The geometric shape of any thing is defined by its boundaries to one or more neighboring things. The notion and description of boundaries thus provides a bridge between mereotopology and the phase-field concept. The present article aims to relate phase-field expressions describing boundaries and especially triple junctions to their Boolean counterparts in mereotopology and contact algebra. An introductory overview on mereotopology is followed by an introduction to the phase-field concept already indicating first relations to mereo- topology. Mereotopological axioms and definitions are then discussed in detail from a phase-field perspective. A dedicated section introduces and discusses further notions of the isConnected relation emerging from the phase-field perspective like isSpatiallyConnected, isTemporallyConnected, isPhysicallyConnected, isPathConnected and wasConnected. Such relations introduce dynamics and thus physics into mereotopology as transitions from isDisconnected to isPartOf can be described.