ObjectiveTo determine whether initial lip asymmetry predicts long-term symmetry changes in patients with unilateral cleft lip and alveolus (UCLA) and to characterize patterns of region-specific morphic change relevant to orthodontic planning.DesignRetrospective observational study.SettingUniversity-based orthodontic clinic.PatientsAmong 80 UCLA patients treated between 2008 and 2023, 42 with standardized frontal photographs at two treatment stages (before active orthodontic treatment [T1] and before comprehensive orthodontic treatment [T2]) under rest and smile conditions were included.Main Outcome MeasuresTen lip-related measures (7 linear distances, 3 angular variables) were obtained from frontal images, and left-to-right asymmetry was calculated as the difference between the noncleft and cleft sides (noncleft-cleft). Longitudinal change was defined as Δ = T2 - T1. Paired t tests with effect sizes (Cohen's dz) and false discovery rate adjustment were used, and importance scores were used to visualize the combined magnitude and robustness of changes.ResultsOverall lip symmetry tended to improve from T1 to T2 in both rest and smile conditions. Measure 2 (peak of Cupid's bow to oral commissure distance) and Measure 6 (lower lip width) exhibited negative Δ values with moderate effect sizes (dz = 0.39-0.42) in unadjusted analyses. After adjustment for multiple comparisons, no comparisons remained statistically significant; however, effect-size patterns suggested consistent, moderate improvement in symmetry in regions around the Cupid's bow.ConclusionsInitial lip asymmetry influences long-term symmetry changes in UCLA patients. Quantitative assessment of region-specific symmetry changes may support interdisciplinary planning focused on individualized soft-tissue outcomes.

Introduction: Several studies have identified transcutaneous spinal cord stimulation (tSCS) as a non-invasive neuromodulation technique for improving motor function in individuals with neurological disorders, including stroke. Despite a plethora of preliminary findings, there remains no standardized protocol regarding the optimal tSCS parameters tailored to patients with stroke. The objective of this study was to employ a supervised machine learning approach to determine the optimal tSCS frequency and intensity parameters for patients with chronic stroke by leveraging data from single-day interventions that systematically varied in frequency and intensity across four stimulation conditions. Methods: Twenty adults with chronic hemiparetic stroke (mean age 53.3 ± 10.8 years; 13 males, 7 females) who were ≥6 months post-stroke was enrolled, excluding individuals with multiple strokes, severe spasticity, or implanted devices. Each participant participated in a baseline session followed by five intervention sessions, during which the frequency and intensity of stimulation were varied randomly. Multimodal sensors, including surface EMG, IMU-based kinematics, and spatiotemporal gait parameters, were used to quantify acute changes in gait symmetry, and optimal stimulation frequency and intensity were defined as those yielding the greatest improvement in the Combined Gait Asymmetry Metric (CGAM). A supervised machine-learning classifier was trained using nested leave-one-subject-out cross-validation to predict the optimal stimulation frequency and intensity to maximize differences from the baseline data alone. AUROC values were calculated for the frequency and intensity predictions. Results: The machine learning models achieved AUROC values of 0.86 [0.75–0.94] for frequency prediction and 0.82 [0.69–0.94] for intensity prediction. The top ten predictive features for each model spanned with spinal motor evoked potentials (sMEPs), wearable sensors, and demographic domains, highlighting multimodal contributions to stimulation optimization. Conclusions: These findings demonstrate that supervised learning can predict individualized tSCS parameters from demographic data and baseline sensor features that yield the greatest improvement in gait symmetry after stroke, representing a promising step toward the data-driven personalization of neuromodulation therapy in neurorehabilitation.

Topological phase transitions provide a unique window into the interplay between structure, magnetism, and Weyl physics in magnetic Weyl semimetals. However, realizing an intrinsic Weyl phase transition between two distinct Weyl states near room temperature remains challenging. Here, we demonstrate that a magnetostructural transition effectively induces such a transition in the kagome magnet Mn3Ga. High-resolution neutron diffraction, magnetization characterizations and first-principles calculations reveal that Mn3Ga undergoes a chiral antiferromagnetic transition below 485 K, followed by a magnetostructural transition to a monoclinic structure with highly canted antiferromagnetic order near room temperature. These cooperative changes in lattice and magnetic symmetries reorganize Weyl nodes, driving a transition from a primary type-II Weyl state to a distinct Weyl state, accompanied by dramatic variations in the anomalous Hall effect and appearance of topological Hall effect. Our findings open a new pathway for discovering novel topological Weyl states andadvancing potential spintronic applications.

A novel quantum insulator-insulator transition was recently reported upon F- doping the Mott insulator CeMnAsO1-x F x . Below the transition, the resistivity increases by more than 2 orders of magnitude over a narrow temperature range, and a colossal Seebeck effect is observed alongside glassy dynamics. A combination of neutron diffraction, heat capacity, and transport measurements has enabled structure-property relationships of the exotic transition to be elucidated. Variable temperature high resolution neutron diffraction shows that there is no change in symmetry at the transition and that the transition can be controlled by increasing the electronic and magnetic coupling between the CeO/F and As-Mn-As blocks. Physical property measurements, combined with first-principles calculations, suggest that the transition is due to the formation of an unusual interlayer excitonic insulator state below the insulator-insulator transition, T II.

Intramuscular vaccination is a routine component of equine medicine, but local muscle soreness may transiently affect gait symmetry. Objective data on vaccination-associated gait changes in horses are lacking. To investigate whether intramuscular vaccination induces measurable gait asymmetries depending on injection site, to inform recommendations on vaccination site selection and short-term exercise management. In this prospective, randomised, blinded, placebo-controlled study, eighteen clinically sound Warmblood horses were enrolled and received an intramuscular vaccination or a 2.0mL saline injection into either the musculus pectoralis descendens or musculus semitendinosus. Objective gait analysis using body-mounted inertial measurement units was performed at baseline and 8, 24, 48, 72 and 96 hours after injection. Vertical displacement asymmetries of the head, withers and pelvis were analysed using predefined clinical relevance thresholds. Fourteen horses were included in the final analysis (pectoralis: nexperimental=8/ncontrol=5; semitendinosus: nexperimental=6/ncontrol=3). Vaccination into the musculus semitendinosus resulted in a transient increase in hindlimb push-off asymmetry. Mean pelvic push-off asymmetry increased from 5.47 mm at baseline to 10.57 mm at 48 hours post-vaccination (P < 0.001) and returned to baseline by 96 hours. No clinically relevant changes in gait symmetry were detected following vaccination into the musculus pectoralis descendens or after saline injection at either site, despite an isolated statistically significant change in the semitendinosus control group at timepoint 96. Vaccination into the musculus semitendinosus resulted in a transient increase in hindlimb push-off asymmetry after 48 hours. These findings support a short reduction in training for at least 72 hours following vaccination.

ABSTRACT High pressure, as a fundamental thermodynamic parameter, can be used as a clean and efficient tool to regulate interatomic distances in quantum materials, enabling precise control of lattice structure, electron correlation, spin–orbit coupling, and band topology without introducing additional chemical impurities. In this review, we summarize that high‐pressure changes in lattice symmetry, orbital hybridization, band structure, magnetic order, and electron–phonon coupling induce the emergence of new quantum states. We also distinguish that high pressure not only compresses lattice structures, but also enhances quantum effects that lead to exotic states, including unconventional superconductivity with elevated transition temperatures, disproportionate charge‐density waves, electron‐correlated driven Mott insulators, topologically protected phases versus stable topologically protected states, and fractional excited quantum spin liquids. In addition, we reconcile the contradictory experimental results in the current research field, such as the nonmonotonic variation of superconducting transition temperature with pressure in kagome metals and the controversial topological phase transition conditions in TaAs. Finally, we outline the potential applications of high‐pressure technologies, including high‐temperature superconductors, quantum computing, and emerging materials.

Manipulation of quantum systems for sensing and transduction rely on controlling the interactions between a quantum system and the many degrees of freedom of the bath. In molecular spin quantum systems, spin-orbit coupling serves as a conduit for energy dissipation via vibrational and phonon modes, which in turn are dictated by changes in oxidation state, metal-ligand covalency, and symmetry of the coordination sphere. The confluence of these factors complicate design strategies however for manipulation of spin qubits for quantum sensing and transduction strategies. Here, we report an investigation of the spin dynamics in isostructural S = 1/2 first-row transition metal complexes in which the spin-orbit coupling is varied between a ls-Co(ii)N4Phen (1-Co) and Cu(ii)N4Phen (1-Cu) complex. Based on free-ion spin-orbit coupling parameters (528 cm-1 for Co(ii) and 829 cm-1 for Cu(ii)), faster spin-lattice relaxation rates (1/T 1) are initially expected for 1-Cuvs.1-Co. However, X-band pulsed EPR and AC susceptibility reveal that both complexes have nearly identical slow spin-lattice relaxation processes. Notably, decoherence (phase memory times, T m) at 60 K is longer for 1-Cu (0.63(1) µs) than for 1-Co (0.56(1) µs). Direct observation of d-d splittings, and determination of anisotropic g-values by EPR spectroscopy reveals an effective decrease in spin-orbit coupling for 1-Cu (λ' = 400-435 cm-1) relative to 1-Co (λ' = 370-400 cm-1) due to greater metal-ligand covalency in the Cu(ii) complex. Computational modelling of spin density distributions (DFT) and the excited state manifolds (CASSCF) support the differences in excited state energies and spin densities that dictate spin dynamics in these complexes. Two sets of nearly degenerate low-frequency modes were identified as possible vibrational relaxation channels via a two-phonon (Raman) process, consistent with contributions from spin-vibrational orbit interactions. This study provides fundamental insight into the role of metal-ligand covalency in modulating spin-orbit coupling contributions to spin-lattice relaxation and decoherence processes. Increased metal-ligand covalency reduces effective spin-orbit coupling, thereby increasing both spin-lattice and coherence time in molecular spin qubits, providing an important strategy for controlling quantum states and spin-vibrational energy transfer processes in molecular qubit platforms for quantum information processing.

Polymorphism, the ability of a compound to crystallize in multiple distinct structures, plays a vital role in determining the physical, chemical, and functional properties of polymorphic materials. While polymorphism enables many critical crystalline materials applications with special properties, predicting such polymorphic structures remains a big challenge. In this study, we analyze structural variations in the Materials Project database, including metastable and pressure-stabilized crystal structures, to explore the topological landscape of polymorphism. Using topological analysis, we identify key statistical patterns in composition, space-group distributions, and polyhedral building blocks. We discover that frequent space group pairs, such as (71,225), display consistent topological patterns across different compounds. We further show that, local polyhedral environments are often conserved across diverse structural variants of a given formula, even as global symmetry and packing arrangements change. By embedding these structures into a topological vector space, we show that structures can cluster together independent of their space group labels. Validation against experimental data from the ICSD confirms that these trends are physically real and not computational artifacts. These findings establish local topological identity as a more robust descriptor than space group symmetry for predicting and classifying structural diversity in inorganic polymorphic systems.

Abstract Further theoretical insights into solid-state electronics of organic crystals are necessary to enable material applications for open-shell molecules. However, the effects of exchange repulsion and the overlap of magnetic orbitals in their crystals have yet to be investigated. In this study, we examine the Br3TOT crystal as a model system featuring a one-dimensional structure with antiferromagnetic ordering and unique functional properties. We conducted a detailed investigation of the electronic states and magnetic properties as well as the effects of expansion and compression, using approximate spin-projected density functional theory with plane-wave basis (AP-DFT/plane-wave). The dependence of the effective exchange integral (J) on the intraradical distance suggests that compression along the stacking direction induces magnetic reversal from antiferromagnetism (AFM) to ferromagnetism (FM). We found that strong exchange repulsion in the crystal is crucial for switching devices that utilize the AFM–FM transition. Furthermore, our results demonstrate that the molecular symmetry changes that accompany expansion and compression are influenced by the symmetry of the crystal structure. The enhanced qualities are associated with a quinone structure, which is important for battery reactions. Consequently, the AP-DFT/plane-wave method showed the importance of exchange repulsion and crystal structures for in silico design of open-shell molecular devices.

Abstract Probing and controlling the stacking order in two-dimensional materials such as graphene and transition metal dichalcogenides plays a critical role in tailoring Moiré bands, band gaps, and associated emergent physical properties. Here, we investigate how stacking-order variations manifest as domains and domain boundaries in epitaxial bilayer graphene, and how these structures are linked to sublattice symmetry at the atomic scale. Using scanning thermoelectric microscopy, we resolve triangular sublattice contrast within Bernal-stacked domains and directly observe its inversion across neighboring regions. At the intervening domain boundaries, the contrast diminishes, indicating restoration of sublattice symmetry through an intermediate AA-type stacking. First-principles calculations of the electronic structure and thermoelectric power reproduce the observed sublattice contrast and predict topological edge states at the domain boundary. These results demonstrate that thermoelectric imaging enables real-space, atomic-resolution probing of stacking-dependent electronic states and the accompanying changes in sublattice symmetry. Moreover, this approach is expected to provide new opportunities for investigating the physical properties of van der Waals multilayer systems.

Simulated gait training improves joint loading symmetry in unilateral transfemoral bone-anchored limb users.

Applying a constant external electric field to a semiconductor nanostructure with Wannier–Mott excitons, in which the electron and hole interact via a centrally symmetric Coulomb potential, alters the symmetry of the system. When the electric field is applied parallel to the z-axis, the system exhibits cylindrical symmetry; when the field lies in the x−y plane, the symmetry is broken. These symmetry changes affect the optical properties of the system. We present a theoretical calculation that yields analytical expressions for the optical functions of CdSe Nanoplatelets—reflectivity, transmissivity, and the absorption coefficient—in an external homogeneous electric field. From these, we focus on the absorption coefficient. We consider various configurations, with the external field oriented perpendicular and parallel to the platelet planes. Using the real density matrix approach, we calculate the linear electro-optical functions of CdSe nanoplatelets, taking into account the effect of dielectric confinement on excitonic states. We also discuss the impact of platelet geometry (thickness and lateral dimensions) and applied field strength on the spectrum.

Crooked nose deformities remain a surgical challenge due to complex asymmetries of bony and cartilaginous structures. The "Hybrid Technique" combines preservation and structural rhinoplasty principles to improve correction while maintaining procedural efficiency. A retrospective study was performed on 54 patients who underwent primary rhinoplasty for crooked nose correction between January 2023 and June 2024. The first 28 consecutive patients were treated with the Pisa Tower technique, and the subsequent 26 with the Hybrid Technique. Baseline demographic and clinical characteristics were comparable between groups. Objective outcomes included nasal axis deviation and R-Webster triangle symmetry measured from standardized photographs and CT scans by two blinded reviewers. Functional results were assessed using the NOSE questionnaire at 12 months.Postoperative changes were analysed using linear regression models adjusted for baseline values, and standardized effect sizes with 95% confidence intervals were calculated to quantify between-group differences. Operative time and postoperative complications were also recorded. Both techniques achieved significant improvement in nasal alignment (p < 0.001). Mean nasal deviation decreased from 8.1° to 1.6° in the Hybrid group and from 7.6° to 1.4° in the Pisa Tower group (p > 0.05). NOSE scores improved markedly in both cohorts (Hybrid: 76.8 → 19.4; Pisa Tower: 74.9 → 21.1; p < 0.001). Postoperative changes in nasal axis deviation and R-Webster triangle symmetry did not differ between groups (p > 0.05). Adjusted effect sizes were small with confidence intervals crossing zero (e.g., nasal axis deviation d = -0.18, 95% CI -0.73 to 0.37), confirming the absence of meaningful between-group differences. NOSE scores improved similarly in both cohorts, and operative time and complications were comparable. Operative time was comparable (119 vs. 122 minutes; p = 0.42). Minor dorsal hump recurrence occurred in one Hybrid and three Pisa Tower cases, with no revisions required. The Hybrid Technique provides reproducible correction of nasal asymmetry with functional outcomes, complication rates, and operative times comparable to the Pisa Tower approach, representing a versatile option for complex nasal deviations.

Understanding the fate of carbonate rocks at mantle depths is crucial for modeling the global carbon cycle. Calcite, CaCO3, undergoes a pressure-induced transition from calcite-I (R3̅c) to calcite-II (P21/c) close to 1.6 GPa, but the effects of these changes on chemical reactivity and electronic properties remain poorly understood. Combining high-pressure X-ray diffraction at the ID27 beamline of the EBS-ESRF synchrotron with charge density analysis reveals subtle electronic and structural changes in the calcite structure with pressure. By determining the integrated charges, atomic basin volumes, and shapes of Ca, C, and O atoms, we effectively decompose the equation of state into individual atomic contributions. The analysis reveals that the phase transition is preceded by a discontinuous charge redistribution between Ca, C, and O atoms, occurring before the symmetry change and reversing upon decompression without hysteresis. Notably, carbon displays negative atomic compressibility, expanding under pressure due to electron uptake, while Ca and O atoms behave conventionally. Our findings demonstrate that experimental charge density methods can resolve pressure-induced electron density rearrangements with unprecedented detail, offering new perspectives on the mineralogy of Earth's interior.

ABSTRACT Competition between phases with different crystal symmetries offers exciting opportunities to achieve unprecedented functionalities. One key challenge is to realize reversible control of phase transition under stimuli. As extensively explored in the benchmark multiferroic BiFeO 3 (BFO), versatile emergent phenomena have been found at the morphotropic phase boundary between ferroelectric rhombohedral (R) and tetragonal phases. In contrast, the transition between polar and antipolar phases in the BFO‐based system has remained largely underexplored. In this work, we demonstrate a reversible and non‐volatile control of antiferroelectric‐ferroelectric phase transition by electric‐field in La‐doped BFO films. An antiferroelectric orthorhombic (O) phase with coexistence of different structural domains is established in as‐grown films. By tuning both the sign and magnitude of the electric field, the successive transitions among antipolar O phase, polar R phase with up and down polarization are achieved, whose reversibility and non‐volatility strongly depend on the La concentration. Moreover, this non‐volatile symmetry change leads to a sign reversal of X‐ray linear dichroism signal, suggesting new opportunities to achieve electric‐field control of magnetic order.

ABSTRACT Context: Up to 36% of patients will develop osteoarthritis within a decade of anterior cruciate ligament reconstruction (ACLR), and post-operative changes in gait mechanics have been shown to be associated with radiographic and biochemical markers of cartilage degeneration. Objective: To characterize changes in limb loading symmetry during walking gait from 6 to 12 months after ACLR in patients with extensor mechanism autografts using force-sensing insoles, and to compare the change in limb loading metrics between patients with bone-patellar tendon-bone (BPTB) and quadriceps tendon (QT) autograft. Design: Prospective cohort study Setting: Orthopaedic rehabilitation clinics Participants: 27 participants (20 female, 13 BPTB, 14 QT, age = 21.4±6.1 years) who underwent unilateral, primary ACLR with BPTB or QT autograft. Main Outcome Measures: Gait assessment, the International Knee Documentation Committee (IKDC) survey, and the ACL-Return to Sport after Injury (ACL-RSI) survey were completed 6±1 and 12±2 months post-ACLR. Results: Participants experienced a significant increase in ACLR limb peak impact force (p=0.007), average loading rate (p=0.043), and instantaneous loading rate (p=0.021) over time, but there were no significant changes in the contralateral limb or LSI. There Participants experienced a significant improvement in IKDC score, but ACL-RSI score did not significantly improve. Conclusions: When tested in the clinical environment using force-sensing insoles, there is an increase in ACLR limb loading from 6 to 12 months post-ACLR, but this change is not impacted by autograft source.

ABSTRACT Context The highest incidences of musculoskeletal (MSK) injuries within the military occur at anatomical regions most impacted by jumping and landing, including the knee. Military personnel assigned to Special Operations Forces (SOF) are at particularly high risk of MSK injury due to occupational demands. Objective To characterize changes in limb loading symmetry during walking gait from 6 to 12 months after ACLR in patients with extensor mechanism autografts using force-sensing insoles, and to compare the change in limb loading metrics between patients with bone-patellar tendon-bone (BPTB) and quadriceps tendon (QT) autograft. Design Cross-Sectional Study Setting Laboratory Patients or Other Participants Two hundred twenty-four uninjured active-duty male SOF personnel (age = 27.7 ± 5.0 years; mass = 83.1 ± 9.1 kg; height = 176.5 ± 5.7 cm) completed biomechanical analyses of two different drop landing tasks (double leg (DLDL) and single leg (SLDL)) and isokinetic strength testing of the quadriceps and hamstrings. Main Outcome Measure(s) Peak hip, knee, and ankle angles; hip, knee, and ankle angles at initial ground contact (@IC); and peak vertical ground reaction (VGRF) forces were identified during landing tasks. Maximum voluntary isokinetic knee extension strength (KES) and knee flexion strength (KFS) were also assessed. Results Participants demonstrated greater KES with their dominant limb by an average of 0.06 Nm/kg (p=0.001, d=0.219) and landed with greater force on the dominant limb during DLDL by an average of 20% bodyweight (p&lt;0.001, d=0.377). No asymmetries involving knee kinematics were identified. During DLDL, both limbs demonstrated similar significant correlations between knee (peak) and ankle (@IC and peak) kinematics and peak VGRF. During nondominant SLDL, knee@IC, peak knee flexion, and peak dorsiflexion significantly correlated to peak VGRF. Peak knee flexion during non-dominant SLDL correlated to non-dominant KES. Conclusions Knee mechanics are important components for shock attenuation, but for this population, factors other than strength likely play a more significant role in controlling the mechanics about the knee during landing tasks.

We uncover a previously unreported solid-solid phase transition in tetrachloro-m-xylene (TCMX), a hexasubstituted benzene derivative exhibiting orientational disorder. Differential scanning calorimetry and powder x-ray diffraction reveal a weak but reproducible phase transition near 437K, corresponding to a continuous, second-order symmetry change from monoclinic P2_{1}/n (phase II) to orthorhombic Pnnm (phase I). Despite this structural reorganization, quasielastic neutron scattering demonstrates that molecular dynamics remain governed by discrete 60^{∘} in-plane reorientational jumps consistent with the pseudosixfold molecular symmetry. The activation energy is unaffected, while only slight variations in relaxation times and effective rotational radii are detected. Molecular dynamics simulations reproduce the transition and clarify its microscopic origin. In phase II, weak orientational correlations between adjacent molecular columns are present, but these constraints vanish in phase I, restoring higher symmetry without altering the underlying reorientational mechanism. This study establishes TCMX as a rare example of a disorder-disorder transition in which molecular dynamics are preserved while collective orientational correlations reorganize. More broadly, our results highlight how subtle symmetry changes govern emergent behavior in disordered crystals, advancing the understanding of plastic phases and phase transitions in complex condensed matter systems.

Mechanical gait asymmetry is a prevalent deficit in many forms of locomotion impairment. Although spatial gait asymmetry adaptations can be elicited with split-belt treadmill training, weight-bearing and propulsion asymmetry remain resistant to improvement. As an alternative approach, we tested asymmetric surface stiffness walking to induce neuromotor adaptation of weight-bearing and propulsion asymmetries. We hypothesized that a bout of asymmetric stiffness walking would elicit aftereffects in the form of asymmetries in weight bearing, propulsion, and plantar flexor activity. Twelve healthy young adults performed a 10-min bout of asymmetric stiffness walking on an adjustable stiffness treadmill. We measured baseline and postperturbation ground reaction forces (GRFs) and spatiotemporal measures during 5-min walking bouts on a dual-belt instrumented treadmill. After asymmetric surface stiffness walking, participants exhibited 2.8% asymmetry in vertical GRF at push off, as well as increased plantarflexor muscle activity (20.7% GAS, 9.5% SOL) during push off on the perturbed side relative to the unperturbed. Participants also decreased their midstance vertical GRF (2.2%) and increased their peak braking GRF (6.8%) on the perturbed side relative to unperturbed. Counter to our hypothesis, they did not increase their propulsion GRF on the perturbed side. We conclude that asymmetric stiffness walking elicited a neuromotor adaptation toward a relative increase in push-off in the target limb, albeit primarily vertically aligned in our cohort of healthy young adults, and that gait adaptation to asymmetric stiffness walking should be investigated in individuals with push-off asymmetries.NEW & NOTEWORTHY Weight-bearing asymmetry in individuals with hemiparetic stroke is resistant to treatments that produce improvements in other gait function measures (e.g., spatiotemporal symmetry). We investigated a novel perturbed ground stiffness intervention applied by an adjustable surface stiffness treadmill and found significant aftereffects in vertical and braking ground reaction force peaks in healthy young adults, as well as increases in perturbed-side plantar flexor activity during push-off, indicating a strong potential for correcting persistent deficiencies in poststroke gait.

Despite of the low transition temperature, the recently identified superconductor CeRh$_2$As$_2$ has garnered significant interest due to its unique symmetry and magnetic characteristics, particularly the existence of two superconducting (SC) phases under a magnetic field, one of which exceeds the Pauli-Clogston limit. The field-induced transition from a low-field even-parity state to a high-field odd-parity state is usually described as a singlet-triplet transition. However, it is uncommon for a single compound to exhibit both triplet and singlet SC scenarios. The aim of this paper is to investigate the possibilities of symmetry changes in the SC state without a change of spin multiplicity. To this end, we construct the SC order parameter based on Anderson pair functions, considering the phase winding within the symmetry of the point group $D_{4h}$ and the magnetic group $4/mm^{\prime }m^{\prime}$. It was found that two triplets with opposite-spin and equal-spin pairing states of symmetry $E_{1u}^{\prime +}$, are nodeless but exhibit distinct internal structures and may be associated with low-and high-field phases. Additionally, nontrivial Cooper pairing resulting from the non-symmorphic structure of the space group was examined, particularly in the case where the Fermi surface intersects with the boundaries of a Brillouin zone (BZ). It was determined that at the X point, triplet pairs are even, while singlet pairs can be either even or odd. Furthermore, at the X point, pair density waves that alter phase by $π$ at the atomic centers linked by lattice translations are also feasible. To explore the possibility of such scenarios, precise DFT calculations of the band structure were performed, revealing the contribution of Ce $4f$ electrons to the states at the Fermi level. Thus, the even-odd transition can take place in a triplet scenario at symmetry points of a BZ.