Differential Probability Research Articles

Differential Condensation of Methane Isotopologues Leading to Isotopic Enrichment under Non-equilibrium Gas-Surface Collision Conditions.

We examine the initial differential sticking probability of CH4 and CD4 on CH4 and CD4 ices under nonequilibrium flow conditions using a combination of experimental methods and numerical simulations. The experimental methods include time-resolved in situ reflection–absorption infrared spectroscopy (RAIRS) for monitoring on-surface gaseous condensation and complementary King and Wells mass spectrometry techniques for monitoring sticking probabilities that provide confirmatory results via a second independent measurement method. Seeded supersonic beams are employed so that the entrained CH4 and CD4 have the same incident velocity but different kinetic energies and momenta. We found that as the incident velocity of CH4 and CD4 increases, the sticking probabilities for both molecules on a CH4 condensed film decrease systematically, but that preferential sticking and condensation occur for CD4. These observations differ when condensed CD4 is used as the target interface, indicating that the film’s phonon and rovibrational densities of states, and collisional energy transfer cross sections, have a role in differential energy accommodation between isotopically substituted incident species. Lastly, we employed a mixed incident supersonic beam composed of both CH4 and CD4 in a 3:1 ratio and measured the condensate composition as well as the sticking probability. When doing so, we see the same effect in the condensed mixed film, supporting an isotopic enrichment of the heavier isotope. We propose that enhanced multi-phonon interactions and inelastic cross sections between the incident CD4 projectile and the CH4 film allow for more efficacious gas–surface energy transfer. VENUS code MD simulations show the same sticking probability differences between isotopologues as observed in the gas–surface scattering experiments. Ongoing analyses of these trajectories will provide additional insights into energy and momentum transfer between the incident species and the interface. These results offer a new route for isotope enrichment via preferential condensation of heavier isotopes and isotopologues during gas–surface collisions under specifically selected substrate, gas-mixture, and incident velocity conditions. They also yield valuable insights into gaseous condensation under non-equilibrium conditions such as occur in aircraft flight in low-temperature environments. Moreover, these results can help to explain the increased abundance of deuterium in solar system planets and can be incorporated into astrophysical models of interstellar icy dust grain surface processes.

S-box Construction Method Based on the Combination of Quantum Chaos and PWLCM Chaotic Map

For a security system built on symmetric-key cryptography algorithms, the substitution box (S-box) plays a crucial role to resist cryptanalysis. In this article, we incorporate quantum chaos and PWLCM chaotic map into a new method of S-box design. The secret key is transformed to generate a six tuple system parameter, which is involved in the generation process of chaotic sequences of two chaotic systems. The output of one chaotic system will disturb the parameters of another chaotic system in order to improve the complexity of encryption sequence. S-box is obtained by XOR operation of the output of two chaotic systems. Over the obtained 500 key-dependent S-boxes, we test the S-box cryptographical properties on bijection, nonlinearity, SAC, BIC, differential approximation probability, respectively. Performance comparison of proposed S-box with those chaos-based one in the literature has been made. The results show that the cryptographic characteristics of proposed S-box has met our design objectives and can be applied to data encryption, user authentication and system access control.

Prevalence of depressive disorders and treatment in China: a cross-sectional epidemiological study

In China, depressive disorders have been estimated to be the second leading cause of years lived with disability. However, nationally representative epidemiological data for depressive disorders, in particular use of mental health services by adults with these disorders, are unavailable in China. The present study, part of the China Mental Health Survey, 2012-15, aims to describe the socioeconomic characteristics and the use of mental health services in people with depressive disorders in China. The China Mental Health Survey was a cross-sectional epidemiological survey of mental disorders in a multistage clustered-area probability sample of adults of Chinese nationality (≥18 years) from 157 nationwide representative population-based disease surveillance points in 31 provinces across China. Trained investigators interviewed the participants with the Composite International Diagnostic Interview 3.0 to ascertain the presence of lifetime and 12-month depressive disorders according to DSM-IV criteria, including major depressive disorder, dysthymic disorder, and depressive disorder not otherwise specified. Participants with 12-month depressive disorders were asked whether they received any treatment for their emotional problems during the past 12 months and, if so, the specific types of treatment providers. The Sheehan Disability Scale (SDS) was used to assess impairments associated with 12-month depressive symptoms. Data-quality control procedures included logic check by computers, sequential recording check, and phone-call check by the quality controllers, and reinterview check by the psychiatrists. Data were weighted according to the age-sex-residence distribution data from China's 2010 census population survey to adjust for differential probabilities of selection and differential response, as well as to post-stratify the sample to match the population distribution. 28 140 respondents (12 537 [44·6%] men and 15 603 [55·4%] women) completed the survey between July 22, 2013, and March 5, 2015. Ethnicity data (Han or non-Han) were collected for only a subsample. Prevalence of any depressive disorders was higher in women than men (lifetime prevalence odds ratio [OR] 1·44 [95% CI 1·20-1·72] and 12-month prevalence OR 1·41 [1·12-1·78]), in unemployed people than employed people (lifetime OR 2·38 [95% CI 1·68-3·38] and 12-month OR 2·80 [95% CI 1·88-4·18]), and in people who were separated, widowed, or divorced compared with those who were married or cohabiting (lifetime OR 1·87 [95% CI 1·39-2·51] and 12-month OR 1·85 [95% CI 1·40-2·46]). Overall, 574 (weighted % 75·9%) of 744 people with 12-month depressive disorders had role impairment of any SDS domain: 439 (83·6%) of 534 respondents with major depressive disorder, 207 (79·8%) of 254 respondents with dysthymic disorder, and 122 (59·9%) of 189 respondents with depressive disorder not otherwise specified. Only an estimated 84 (weighted % 9·5%) of 1007 participants with 12-month depressive disorders were treated in any treatment sector: 38 (3·6%) in speciality mental health, 20 (1·5%) in general medical, two (0·3%) in human services, and 21 (2·7%) in complementary and alternative medicine. Only 12 (0·5%) of 1007 participants with depressive disorders were treated adequately. Depressive disorders in China were more prevalent in women than men, unemployed people than employed, and those who were separated, widowed, or divorced than people who were married or cohabiting. Most people with depressive disorders reported social impairment. Treatment rates were very low, and few people received adequate treatment. National programmes are needed to remove barriers to availability, accessibility, and acceptability of care for depression in China. National Health Commission and Ministry of Science and Technology of People's Republic of China. For the Chinese translation of the abstract see Supplementary Materials section.

Erratum in: Decoding binary decisions under differential target probabilities from pupil dilation: A random forest approach.

Erratum in: Decoding binary decisions under differential target probabilities from pupil dilation: A random forest approach.

Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models

We propose a novel blocked version of the continuous-time bouncy particle sampler of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855–867, 2018) which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state-space models (Singh et al. in Biometrika 104(4):953–969, 2017) and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state-space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. (J R Stat Soc Ser B Stat Methodol 72(3):269–342, 2010), is illustrated numerically for both simulated data and a challenging real-world financial dataset.

A secure key dependent dynamic substitution method for symmetric cryptosystems.

The biggest challenge for symmetric cryptosystems is to replace their static substitution with dynamic substitution, because static substitution S-boxes make the symmetric block ciphers more vulnerable to attacks. Previous well-known dynamic key-dependent S-boxes are lacking in dynamicity and do not provide optimal security for symmetric block ciphers. Therefore, this research aims to contribute an effective and secure method for designing key-dependent dynamic S-box with dynamic permutations to make the symmetric block ciphers optimally secure. The proposed S-box method has been experimentally evaluated through several measures such as bit independence criteria, non-linearity, hamming distance, balanced output, strict avalanche criteria including differential and linear approximation probabilities. Moreover, the randomness properties of proposed method have also been evaluated through several standard statistical tests as recommended by the National Institute of Standards and Technology (NIST). Thus, the results show that the proposed method, not only retains effective randomness properties but it also contains, good avalanche effect (up to 62.32%) which is significantly improved than others. Therefore, the proposed substitution method is highly sensitive to the secret key because, only a single bit change in key generates an entirely new S-box with all 256 values at different positions. Thus, the overall evaluation shows that the proposed substitution method is optimally secure and outperforming as compared to the existing S-box techniques. In future, the proposed method can be extended for different key sizes (192–256 bits) or even more.

Decoding binary decisions under differential target probabilities from pupil dilation: A random forest approach.

Although our pupils slightly dilate when we look at an intended target, they do not when we look at irrelevant distractors. This finding suggests that it may be possible to decode the intention of an observer, understood as the outcome of implicit covert binary decisions, from the pupillary dynamics over time. However, few previous works have investigated the feasibility of this approach and the few that did, did not control for possible confounds such as motor-execution, changes in brightness, or target and distractor probability. We report on our efforts to decode intentions from pupil dilation obtained under strict experimental control on a single trial basis using a machine learning approach. The basis for our analyses are data of 69 participants who looked at letters that needed to be selected with stimulus probabilities that varied systematically in a blockwise manner (n = 19,417 trials). We confirm earlier findings that pupil dilation is indicative of intentions and show that these can be decoded with a classification performance of up to 76% area under the curve for receiver operating characteristic curves if targets are rarer than distractors. To better understand which characteristics of the pupillary signal are most informative, we finally compare relative feature importances. The first derivative of pupil size changes was found to be most relevant, allowing us to decode intention within only about 800 ms of trial onset. Taken together, our results provide credible insights into the potential of decoding intentions from pupil dilation and may soon form the basis for new applications in visual search, gaze-based interaction, or human–robot interaction.

Multilevel information fusion for cryptographic substitution box construction based on inevitable random noise in medical imaging

Block cipher has been a standout amongst the most reliable option by which data security is accomplished. Block cipher strength against various attacks relies on substitution boxes. In literature, extensively algebraic structures, and chaotic systems-based techniques are available to design the cryptographic substitution boxes. Although, algebraic and chaotic systems-based approaches have favorable characteristics for the design of substitution boxes, but on the other side researchers have also pointed weaknesses in these approaches. First-time multilevel information fusion is introduced to construct the substitution boxes, having four layers; Multi Sources, Multi Features, Nonlinear Multi Features Whitening and Substitution Boxes Construction. Our proposed design does not hold the weakness of algebraic structures and chaotic systems because our novel s-box construction relies on the strength of true random numbers. In our proposed method true random numbers are generated from the inevitable random noise of medical imaging. The proposed design passes all the substitution box security evaluation criteria including Nonlinearity, Bit Independence Criterion (BIC), Strict Avalanche Criterion (SAC), Differential Approximation Probability (DP), Linear Approximation Probability (LP), and statistical tests, including resistance to Differential Attack, Correlation Analysis, 2D, 3D histogram analysis. The outcomes of the evaluation criteria validate that the proposed substitution boxes are effective for block ciphers; furthermore, the proposed substitution boxes attain better cryptographic strength as compared to very recent state-of-the-art techniques.

Teen dating violence: From analyzing the problem to finding solutions.

Teen dating violence: From analyzing the problem to finding solutions.

Resonant Effect of High-Energy Electron–Positron Pairs Production in Collision of Ultrarelativistic Electrons with an X-ray Electromagnetic Wave

The process of resonant high-energy electron–positron pairs production by electrons in an X-ray pulsar electromagnetic field is studied theoretically. Under the resonance conditions, the second-order process under consideration effectively reduces into two sequential first-order processes: X-ray-stimulated Compton effect and X-ray–stimulated Breit–Wheeler process. The kinematics of the process is studied in detail: the dependencies of the energy of the scattered electron on its outgoing angle and the energies of the particles of the pair on the outgoing angle of the scattered electron and the opening angle of the pair are obtained. The analysis of the number of different possible particles energies values in the entire range of the angles is also carried out, according to which the energies of the particles of the pair can take up to eight different values at a fixed outgoing angle of the scattered electron and opening angle of the pair. The estimate of the resonant differential probability per unit time of the process, which reaches the maximum value of 24 orders of the value of the non-resonant differential probability per unit time, is obtained. The angular distribution of the differential probability per unit time of the process is analyzed, particularly for the case of high-energy positrons presenting in pulsar radiation.

Maximums of the Additive Differential Probability of Exclusive-Or

At FSE 2004, Lipmaa et al. studied the additive differential probability adp⊕(α,β → γ) of exclusive-or where differences α,β,γ ∈ Fn2 are expressed using addition modulo 2n. This probability is used in the analysis of symmetric-key primitives that combine XOR and modular addition, such as the increasingly popular Addition-Rotation-XOR (ARX) constructions. The focus of this paper is on maximal differentials, which are helpful when constructing differential trails. We provide the missing proof for Theorem 3 of the FSE 2004 paper, which states that maxα,βadp⊕(α,β → γ) = adp⊕(0,γ → γ) for all γ. Furthermore, we prove that there always exist either two or eight distinct pairs α,β such that adp⊕( α,β → γ) = adp⊕(0,γ → γ), and we obtain recurrence formulas for calculating adp⊕. To gain insight into the range of possible differential probabilities, we also study other properties such as the minimum value of adp⊕(0,γ → γ), and we find all γ that satisfy this minimum value.

Optimizing S-box generation based on the Adaptive Agent Heroes and Cowards Algorithm

This paper introduces a new variant of a metaheuristic algorithm based on Agent Heroes and Cowards Algorithm (AHC), called Adaptive Agent Heroes and Cowards Algorithm (AAHC). The main feature of AAHC is the fact that the algorithm allows adaptive assignment of its population agents into cowards and heroes based on the exponential controlling functions. Furthermore, unlike its predecessor, AAHC also permits systematic manipulation of candidate solutions around the global best agent via the swap operator to boost its search intensification process. Meanwhile, to further enhance the diversification its solution, AHC also exploit the Tent map as the pseudo random generator replacement during its initial population initialization. Experimental results based on the generation of 8 × 8 substitution-box demonstrate that the proposed AAHC outperforms other competing metaheuristic algorithms in two main S-box criteria namely nonlinearity and strict avalanche criteria whilst maintaining commendable performances on bits independence criteria, differential approximation probability, linear approximation probability and transparency order.

Mullerianosis of the urinary bladder; A case report.

IntroductionMullerianosis is a sporadic condition of the urinary bladder. The study aims to present a case of mullerianosis with a brief literature review.Case presentationA 52-year-old lady presented with hematuria for one-year duration. A general urine examination showed microscopic hematuria. Abdominal and transvaginal ultrasonography revealed a soft tissue mass (13 * 10 mm) within the base of the urinary bladder. Cystoscopy showed 1.0 * 1.3 cm benign-looking mass bulging into the posterior bladder wall covered by a normal bladder mucosa. Transurethral resection was done. The histopathological examination was consistent with mullerianosis.DiscussionTwo hypotheses have been proposed; the first one (implantation theory) believing that at the time of pelvic surgery and caesarian delivery Mullerian tissues become implanted inside the bladder. The second theory (metaplastic theory) holds the probability of differentiation of Mullerian epithelium to endometrial, endocervical, and tubal components and proliferation in the bladder.Conclusionmullerianosis is a very infrequent entity that mainly affects the urinary bladder and is mainly reported in females during the reproductive period, medical and surgical treatment are both regarded as the management options.

S-Box Construction Method Based on the Combination of Quantum Chaos and PWLCM Chaotic Map

For a security system built on symmetric-key cryptography algorithms, the substitution box (S-box) plays a crucial role to resist cryptanalysis. In this article, we incorporate quantum chaos and PWLCM chaotic map into a new method of S-box design. The secret key is transformed to generate a six tuple system parameter, which is involved in the generation process of chaotic sequences of two chaotic systems. The output of one chaotic system will disturb the parameters of another chaotic system in order to improve the complexity of encryption sequence. S-box is obtained by XOR operation of the output of two chaotic systems. Over the obtained 500 key-dependent S-boxes, we test the S-box cryptographical properties on bijection, nonlinearity, SAC, BIC, differential approximation probability, respectively. Performance comparison of proposed S-box with those chaos-based one in the literature has been made. The results show that the cryptographic characteristics of proposed S-box has met our design objectives and can be applied to data encryption, user authentication and system access control.

Temporal coherent control of resonant two-photon double ionization of the hydrogen molecule via doubly excited states

We use time-delayed, counter-rotating, circularly polarized few-cycle attosecond nonoverlapping pulses to study the temporal coherent control of the resonant process of two-photon double ionization (TPDI) of hydrogen molecule via doubly excited states for pulse propagation direction along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}$ either parallel or perpendicular to the molecular axis $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$. For $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}\ensuremath{\parallel}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$ and a pulse carrier frequency of 36 eV resonantly populating the ${Q}_{2}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$ doubly excited state as well as other $^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}$ doubly excited states, we find that the indirect ionization pathway through these doubly excited states changes the character of the kinematical vortex-shaped momentum distribution produced by the two direct ionization pathways from fourfold to twofold rotational symmetry. This result is similar to what found in TPDI of the He atom involving $^{1}P_{\ifmmode\pm\else\textpm\fi{}1}^{o}$ doubly excited states [Ngoko Djiokap and Starace, J. Opt. 19, 124003 (2017)]; however, angular distributions exhibiting a quantum beat effect between the ground state and a doubly excited state seen for the He atom are observed here for its molecular counterpart with an anomaly in shape and magnitude, not in frequency. The sixfold differential probability integrated over the azimuthal angle of the photoelectron pair shows that this anomaly is due to autoionization decays and quantum beats between doubly excited states. For $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}\ensuremath{\perp}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{R}}$ and a broadband pulse carrier frequency of 30 eV populating the ${Q}_{1}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$, ${Q}_{1}^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}(1)$, ${Q}_{2}^{1}\mathrm{\ensuremath{\Pi}}_{u}^{+}(1)$, and ${Q}_{1}^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}(2)$ doubly excited states, the momentum distribution is shown to exhibit dynamical electron vortices with four spiral arms, which originates from the interplay between the $^{1}\mathrm{\ensuremath{\Delta}}_{g}^{+}$, $^{1}\mathrm{\ensuremath{\Pi}}_{g}^{+}$, and $^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ dynamical ionization amplitudes. Our treatment within either the adiabatic-nuclei approximation or fixed-nuclei approximation shows that the latter provides a very good account for this correlated process.

Large fluctuations in multi-scale modeling for rest hematopoiesis.

Hematopoiesis is a biological phenomenon (process) of production of mature blood cells by cellular differentiation. It is based on amplification steps due to an interplay between renewal and differentiation in the successive cell types from stem cells to mature blood cells. We will study this mechanism with a stochastic point of view to explain unexpected fluctuations on the mature blood cell number, as surprisingly observed by biologists and medical doctors in a rest hematopoiesis. We consider three cell types: stem cells, progenitors and mature blood cells. Each cell type is characterized by its own dynamics parameters, the division rate and the renewal and differentiation probabilities at each division event. We model the global population dynamics by a three-dimensional stochastic decomposable branching process. We show that the amplification mechanism is given by the inverse of the small difference between the differentiation and renewal probabilities. Introducing a parameter K which scales simultaneously the size of the first component, the differentiation and renewal probabilities and the mature blood cell death rate, we describe the asymptotic behavior of the process for large K. We show that each cell type has its own size and time scales. Focusing on the third component, we prove that the mature blood cell population size, conveniently renormalized (in time and size), is expanded in an unusual way inducing large fluctuations. The proofs are based on a fine study of the different scales involved in the model and on the use of different convergence and average techniques in the proofs.

Accelerating the Search of Differential and Linear Characteristics with the SAT Method

The introduction of the automatic search boosts the cryptanalysis of symmetric-key primitives to some degree. However, the performance of the automatic search is not always satisfactory for the search of long trails or ciphers with large state sizes. Compared with the extensive attention on the enhancement for the search with the mixed integer linear programming (MILP) method, few works care for the acceleration of the automatic search with the Boolean satisfiability problem (SAT) or satisfiability modulo theories (SMT) method. This paper intends to fill this vacancy. Firstly, with the additional encoding variables of the sequential counter circuit for the original objective function in the standard SAT method, we put forward a new encoding method to convert the Matsui’s bounding conditions into Boolean formulas. This approach does not rely on new auxiliary variables and significantly reduces the consumption of clauses for integrating multiple bounding conditions into one SAT problem. Then, we evaluate the accelerating effect of the novel encoding method under different sets of bounding conditions. With the observations and experience in the tests, a strategy on how to create the sets of bounding conditions that probably achieve extraordinary advances is proposed. The new idea is applied to search for optimal differential and linear characteristics for multiple ciphers. For PRESENT, GIFT-64, RECTANGLE, LBlock, TWINE, and some versions in SIMON and SPECK families of block ciphers, we obtain the complete bounds (full rounds) on the number of active S-boxes, the differential probability, as well as the linear bias. The acceleration method is also employed to speed up the search of related-key differential trails for GIFT-64. Based on the newly identified 18-round distinguisher with probability 2−58, we launch a 26-round key-recovery attack with 260.96 chosen plaintexts. To our knowledge, this is the longest attack on GIFT-64. Lastly, we note that the attack result is far from threatening the security of GIFT-64 since the designers recommended users to double the number of rounds under the related-key attack setting.

Strong Differential Photoion Circular Dichroism in Strong-Field Ionization of Chiral Molecules.

We investigate the differential ionization probability of chiral molecules in the strong-field regime as a function of the helicity of the incident light. To this end, we analyze the fourfold ionization of bromochlorofluoromethane (CHBrClF) with subsequent fragmentation into four charged fragments and different dissociation channels of the singly ionized methyloxirane. By resolving for the molecular orientation, we show that the photoion circular dichroism signal strength is increased by 2 orders of magnitude.

Absorption and analysis of unbound quantum particles one by one

In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied on truncated numerical domains -- at the cost of losing information. Here we present methods for calculating differential probabilities for unbound particles which are subjected to a {\it complex absorbing potential}. In addition to attenuating outgoing waves, this absorber is also used to probe them by projection onto single-particle scattering states, thus rendering the calculation of multi-particle scattering states superfluous. Within formalism based on the Lindblad equation, singly differential spectra from subsequent absorptions are obtained by resolving the dynamics of the remaining particles after the first absorption. While the framework generalizes naturally to any number of particles, explicit, compact and intuitive expressions for the differential probability distributions are derived for the two-particle case. The applicability of the method is illustrated by numerical examples involving two-particle model-systems. These examples, which address scattering and photo ionization, demonstrate how energy distributions of unbound particles may be determined on numerical domains considerably smaller than the actual extension of the system.

Unveiling the transverse formation length of nonlinear Compton scattering

The process of emission of electromagnetic radiation does not occur instantaneously but it is "formed" over a finite time known as radiation formation time. In the ultrarelativistic regime, the corresponding (longitudinal) formation length is given by the formation time times the speed of light and controls several features of radiation. Here, we elucidate the importance of the transverse formation length (TFL) by investigating nonlinear Compton scattering by an electron initially counterpropagating with respect to a \emph{flying focus} laser beam. The TFL is related to the transverse size of the radiation formation "volume" and, unlike the longitudinal formation length, has a quantum origin. Being the TFL typically of the order of the Compton wavelength, where any laser field can be assumed to be approximately uniform, related quantum interference effects have been ignored. However, we show analytically that if the focus in a flying focus beam with $n_L\gg 1$ cycles moves at the speed of light and backwards with respect to the beam propagation direction, the effects of the TFL undergo a large enhancement proportional to $n_L$ and may substantially alter the differential emission probability for feasible flying focus pulses.